The service, wwould see a nearby postmaster – in this case from Denholm – provide a service at a set time each week.
It will also serve Broughton, near Biggar.
The Innerleithen mobile service would operate from the Co-op, Peebles Road, Innerleithen, and would visit every Friday between 9.30am and 1pm.
The new service would replace the previous one, which ceased on February 9, following the resignation of the postmaster.
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Customers can collect benefits in cash using everyday banking services or their Post Office card account.
The Post Office is now inviting customers and interested parties to give their comments on the move before the consultation closes on March 24.
Kenny Lamont, post office area manager, said: “We are confident that this new service at the heart of the local community will meet customer needs.
“The introduction of a mobile outreach service presents the best possible solution to allow us to maintain Post Office services in Broughton and Innerleithen in the longer term.”
During the public consultation, the Post Office welcomes feedback on any issues customers would like considered before a final decision is taken on this proposal.
Submissions can be made during the consultation by Freepost YOUR COMMENTS to Post Office Ltd, via email to [email protected], via the Customer Helpline on 03457 223344 or textphone 03457 223355.
Customers can also share their views online through the quick and easy questionnaire at postofficeviews.co.uk with the branch code Broughton – 13382499 & Innerleithen – 19683099.
The move is part of an investment on £1.34billion – an investment for the Post Office network to undertake a transformation programme across 6,000 branches.