However, they have denied that it will impact on the overall cost of the Borders rail project which is estimated at between £235million and £295million.
It followed the discovery of underground power cables at the site of the proposed terminus.
Last month, we revealed Transport Scotland - the national agency in charge of overseeing the rebuilding of a 35-mile section of the former line between Edinburgh and the Borders - was consulting on plans to move the station closer to Galashiels.
Community councillors rejected the proposal amid fears over the impact it could have on the village.
However, this month, transport chiefs claimed the cost of moving the cables to accommodate the station in Tweedbank, which they had previously only stated would be a "significant sum", could put the whole project to re-establish passenger rail services in the Borders for the first time in more than 40 years at risk.
Speaking at this month's meeting of Tweedbank Community Council, project manager Andrew Mackie, from Transport Scotland, said: "Millions of pounds of taxpayers money are going to be wasted if we have to move the cables three or four metres (to accommodate the station on the original site) and this is one of the top risks of rebuilding the railway."
But he added: "We think we can maintain the quality of life for residents in Tweedbank with this new design."
It is envisaged moving the terminus from its original site, opposite the junction to the industrial estate nearest Craw Wood, to a cutting behind the entrance to Essenside Drive, with a pedestrian entrance opposite Blakehope Court - although the road entrance would remain at a new roundabout to be built at the opposite end of Tweedbank Drive.
However, concerns have been raised that it could lead to an increase in traffic through the village, as well as rogue parking in the surrounding streets, and put lives at risk.
And the community council, who have also raised concerns over the impact the station will have on noise and the local wildlife, have urged a rethink.
Chairman John Cavaroli said: "We, as a community council, are fully supportive of plans to re-establish the railway in the Borders. But it is our duty to protect the village."
Nevertheless he added: "I'm sure if you suggested some traffic calming measures along Tweedbank Drive then people in the village may be more inclined to support the moving of the platform."
Roads chiefs from Scottish Borders Council, who were also in attendance at the meeting, revealed they could monitor the flow of traffic once the station was opened and, if there were any problems with motorists speeding or parking on verges, they could talk about introducing various traffic management measures - such as building bollards, chicanes and speed bumps.
However, despite expecting around 50,000 passengers to use the line in its first year, they insisted any increase in traffic through the village would be "minimal".
Robert Young, the local authority's head of roads and infrastructure, explained that a recent survey showed 2800 cars used Tweedbank Drive each day.
And, despite no park and ride facility planned at the neighbouring station in Galashiels, he revealed he only anticipated 100 cars would use the free car park at the station in Tweedbank, which will have a capacity to cope with up to 280 cars, on its first day of opening.
Mr Young, who also revealed the project team had a duty to ensure the noise produced by the railway did not exceed agreed levels, said: "I don't think there are any significant disadvantages with the new positioning of the platform.
"If noise is a concern then there is a significant buffer area between the station and neighbouring houses."
And he added: "We could also put up signage directing motorists along the bypass to reduce the amount of traffic through the centre of the village."
Community councillors heard similar efforts to discourage heavy goods vehicles motoring through Tweedbank en route to the village's industrial estate had proved unsuccessful and controversial plans to block access, by closing Tweedbank Drive at its junction with Craw Wood so Tweedbank industrial estate was only accessible from Melrose, had met with local opposition.
Councillor John Paton-Day, who represents the area on Scottish Borders Council, said: "Where the station is isn't a problem to me but start traffic calming measures now. They would certainly cost less than moving the cables." But he added: "I don't like bumps in the road - I think they are deadly."
The Borders Railway project team presented their plans to Tweedbank Community Council at their meeting in the community centre last month.
And, this month, they returned to address their concerns.
Mr Cavaroli said he did not think moving the terminus closer to the village, as it stood, was the best option.
However, the project director, Steve Milligan, from Transport Scotland, argued it was the best option for the public because it would save millions of pounds of taxpayers money.
He also revealed an environmental officer had been appointed to oversee the building of the line and has the power to stop works should there be any concerns over the impact they will have on local wildlife.
Meanwhile, Transport Scotland has been unable to guarantee that the so-called red bridge, which will carry the railway over the River Tweed, will be kept open throughout the two and a half year construction phase.
The popular walkway, which links Tweedbank with Langlee, is part of the Southern Upland Way - Scotland's only coast to coast footpath.
However, Jonathan Hepton, the Borders Railway community liaison manager, pointed out the bridge is a listed building and any works planned would be "minimal".
Community councillor Vivien Lowther said: "I hate to say it but I don't feel like we're going to get an option. I suspect your visit is just a paper exercise. We have concerns over road safety and parking but they seem to be negligible. I think what you are really saying is that the cost of moving the cables is too high so we don't really have a choice."
It is understood the cost of moving the underground power cables is around £2million.
Community councillor Jean Honeyman questioned how the problem had not been raised when the plans to reopen the rail link were first drawn up more than a decade ago.
Mr Mackie said the project team was aware of the problems posed by the cables but it was only recently, following discussions with Scottish Power, that the cost and practicalities of moving them had become clear.
However, transport chiefs admitted they could not confirm the exact location of the cables until trial pits are dug later this year, leading to uncertainty over the siting of the new station.
Mr Milligan, who stressed the plans on show were only draft proposals, said: "This is not set in stone.
"This is us consulting way in advance. What we have given you now is indicative of what we think it might look like but a contractor could come up with something completely different."
But he added: "We have heard what you have to say and will relay that to the successful bidder."
The Borders Railway will re-establish passenger railway services between Edinburgh and Tweedbank for the first time since 1969. The current target for completing the line is 2014.
Three organisations have been selected to submit tenders for the multi-million pound rail link project. The BAM, IMCD and New Borders Railway bids include a wide range of financial and construction companies.
And it is hoped a contract to construct the rail route can be awarded late next year.