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."

The move by Flintshire council is partly aimed at increasing recycling rates to meet Welsh Government targets.
A report to the council's cabinet said if enforcement action fails, it will need to reconsider introducing three-weekly bin collections.
From June 2017, all rubbish will need to go into wheelie bins and anything else will not be collected.
Then from September, anyone still leaving rubbish outside bins will face fixed penalty notices.

The 24-year-old was under contract with the Stags, but Marcus Bignot's side have reached an agreement to bring him in on a free transfer.
He spent the first half of the season on loan at Crawley, scoring three goals in 23 appearances.
The ex-Burton player will officially join on 1 January and becomes Bignot's first signing for the Mariners.

Raqqa Is Being Slaughtered Silently (RBSS) said Ahmad Mohammed al-Mousa was killed by a group of masked men in the rebel-held city of Idlib on Wednesday.
The group have no further details, but at least two other members have been killed by IS militants since 2014.
RBSS was honoured last month by the Committee to Protect Journalists (CPJ).
The New York-based organisation condemned Mr Mousa's murder.
"Just a few weeks ago, nearly 900 journalists, press freedom advocates, and supporters attending CPJ's International Press Freedom Awards stood together in solidarity with Raqqa Is Being Slaughtered Silently. Today we are all standing together again, this time in mourning," said CPJ Executive Director Joel Simon.
Earlier this year, IS claimed responsibility for the kidnapping of Mr Mousa's father and four other Syrians accused of being members of RBSS.
In October, RBSS member Ibrahim Abdul Qader was killed by IS militants, along with fellow journalist Fares Hamadi, in south-eastern Turkey.
IS subsequently published a video showing one of the men with his throat cut, and warned: "You will not be safe from the knife of the Islamic State. Our hand will reach you wherever you are."
RBSS is one of the few independent sources of news left in the northern Syrian city of Raqqa, which IS has controlled since August 2013 and serves as the de facto capital of the "caliphate" whose creation the group proclaimed in June 2014.

Forster, who rejoined the club in July after 22 games on dual registration at Haven earlier in his career, replaces sacked James Coyle.
He began his career at Saints, winning the academy Grand Final there, but was limited to five senior appearances.
"This appointment will lift everybody," general manager Amanda Hewer said.
The ex-Salford forward takes charge after a season which saw Haven relegated from the Championship, despite winning three of the final five games in the Super 8s.
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Transport officials from the Scottish government have held talks on the possibility of extending the Borders Railway beyond Tweedbank.
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Householders who persistently leave out too much rubbish in Flintshire will face fines from next year.
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Grimsby have signed striker Adi Yussuf on an 18-month deal from fellow League Two side Mansfield.
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Another member of a Syrian activist group that reports on the activities of the jihadist group Islamic State (IS) in the city of Raqqa has been murdered.
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Whitehaven have appointed former St Helens prop Carl Forster as player-coach at the age of 24, the youngest in the professional game.