The Scottish government has confirmed the prospect would be explored as part of a planned feasibility study.
The commitment has come from Infrastructure Secretary Keith Brown.
He was replying to a written parliamentary question tabled by south of Scotland MSP, Joan McAlpine.
The Borders Railway between Edinburgh and Tweedbank opened to the public earlier this year.
In his response,  Mr Brown said the Scottish government remained committed to supporting the development of a feasibility study on extending the route through to Carlisle.
He said the south east transport partnership, SEStran, planned to appoint a contractor early next year to carry out the initial research.
The Scottish government is also working with the regional transport partnership, local councils and Network Rail on what post-feasibility work would be required to prepare a business case to satisfy current transport guidelines.
Langholm was not on the old Waverley line which was shut in 1969 but was served by a branch line from the railway.
It opened on 1864 and closed to passengers a century later.
A station in Langholm will be considered as part of a potential future extension of the Borders Railway to Carlisle.