Ms Grahame met with the Community Land Advisory Service this week in Parliament and discussed the benefits of food growing and allotments for the local community.
She said: "We have allotments in my constituency, and I would mention Walkerburn in particular and these have made a massive difference to the community. The whole are has improved because of the allotment but we could still do with more space.
"Many children don't know anything about growing their own fruit and vegetables and this is down to the fact that many modern housing developments have very small gardens."
Ms Grahame will now contact Scottish Borders and Midlothian Councils to see what availability there would be for allotments to be developed.
She added: "I am one of the many people in Scotland on a waiting list for an allotment and in Peebles there are four sites for allotments, 42 allotments and a 10-year waiting list. In Midlothian only Auchendinny near Penicuik, as far as I know, has allotments and again there is a 10-year waiting list.
"This proves there is a genuine need for more land to be made available for allotments and would give people the opportunity to eat organically grown food, cut down on food miles to the supermarket, get healthy exercise and educate our children about where food comes from."