The idea will be looked at as part of a wider study of transport issues across southern Scotland.
Campaign for Border Rail spokesman Simon Walton said they would have preferred a report looking solely at rail services in the area.
However, he said it was welcome progress nonetheless.
Transport Scotland announced earlier this week that it intended to award the contract to look at wider transport issues across the south of the country to Jacobs UK Ltd.
It is hoped the study can get under way later this month and will take about seven months to complete.
Mr Walton said it was good to see the CBR's case for extending the railway was being recognised.
"It is a first step if not exactly a giant leap - it is certainly a move in the right direction," he said.
"We at the CBR would have been happier with a feasibility study looking solely at railway extension but this is a positive move.
"It does back our findings that it makes sense locally, socially and strategically to take the railway through Hawick and on to Carlisle."

Four councils have pledged £250,000 for a detailed traffic modelling plan to look at traffic on both sides of the proposed bridge in detail.
The idea for a new bridge to ease congestion in Reading town centre has been circulating for about 40 years.
There are three main routes over the Thames in the area, two in Caversham, Reading and one in Sonning, Wokingham.
Wokingham and Reading Borough Councils, along with Oxfordshire County Council and South Oxfordshire District Council have all pledged money for the study.
A spokesman for South Oxfordshire District Council said: "We are mindful of the potential negative impact that a scheme such as and additional bridge could have on the road network within South Oxfordshire.
"However we are committed to working with neighbouring authorities to identify solutions which may ease the traffic problems."
Wokingham council leader Keith Baker, said other ideas to ease the traffic congestion including an expanded park-and-ride route were "tinkering at the edges - we need to do something big".
Mr Baker said: "We've had an extensive traffic model for our area but what we didn't have was going across the river into Oxfordshire.
"That hopefully will give us the definitive evidence to start mitigating against some of the issues that Oxfordshire County Council have."
The bridge and any road alterations would cost between £60m and £100m, which would require government funding.

"I wasn't 100% sober," she said at an event with fellow Justice Antonin Scalia.
She said she "couldn't resist the fine wine" at the dinner which traditionally brings together some of the court's justices before the speech.
At 81, Justice Ginsburg is the oldest serving judge on the Supreme Court.
She was asked about the incident by the moderator at an event at George Washington University on Thursday evening.
Justice Ginsburg was repeatedly pictured slumbering in her chair as President Barack Obama addressed the joint session of Congress in the House of Representatives on 20 January.
"The audience for the most part is awake, but they're bobbing up and down all the time. And we sit there as stone-faced, sober judges. But we're not.
"At least I wasn't 100% sober when we went to the State of the Union," she said, provoking audience laughter.
Justice Ginsburg said she had vowed to stick to sparkling water after dozing at the speech in past years, but was unable to resist the lure of a "very fine California wine" brought by Justice Anthony Kennedy.
"In the end, the dinner was so delicious it needed wine," she said.
"Well, that's the first intelligent thing you've done," quipped Justice Scalia.
Former Justice David Souter used to give her a pinch when he spotted the warning signs in years gone by, Justice Ginsburg said, but the judges beside her this time were "more timid".
Borders Railway campaigners have welcomed moves to examine the possibility of extending the route to Carlisle.
[NEXT_CONCEPT]
A feasibility study into a third River Thames bridge in the Reading area has been given council backing.
[NEXT_CONCEPT]
US Supreme Court Justice Ruth Bader Ginsburg has admitted there is a reason she was seen nodding off at the president's State of the Union address.