Infrastructure minister Keith Brown has confirmed that officers have discussed a feasibility study on linking the rail line with Carlisle, through Hawick.
News of the discussions emerged in response to a parliamentary question tabled by MSP Jim Hume.
The new 30-mile Borders Railway is expected to open in September.
In answer to Mr Hume's question, Mr Brown said the government had played an active part in taking forward the Borders Railway Blueprint for the Future.
He added: "Transport Scotland officials have already met with partners and offered initial advice on a scoping document which will explore the possibility of extending the Borders railway towards Hawick and Carlisle."
The announcement was welcomed by the Lib Dem MSP for the south of Scotland.
Mr Hume said: "I have no doubt that such a project would greatly benefit communities not just in the Borders but also in Dumfriesshire, and would draw even further on the already clear tourism opportunities from the line reaching Tweedbank.
"Local campaigners such as the Campaign for Borders Rail have kept the focus on this issue and this positive response from the Scottish government must now be the building blocks for progress on an extended rail link.
"I will continue to encourage Ministers to drive the initiative forward."
Transport officials from the Scottish government have held talks on the possibility of extending the Borders Railway beyond Tweedbank.