Mr Stevenson said the route could be extended beyond Tweedbank
A reopened rail line between Edinburgh and the Borders could be extended to Carlisle, according to the Scottish transport minister.
Stewart Stevenson said it was a "perfectly reasonable ambition" that the route might stretch into England.
The process to find a contractor to build the line to Tweedbank in the Borders started last week.
It is hoped a deal for the £295m project can be awarded in 2011 with completion of the route due in 2014.
Mr Stevenson said the railway could be an economic boost for the south of Scotland.
He added that it could ultimately be extended to reach the north of England.
"That's a perfectly reasonable ambition, Carlisle used to be a very important staging point for the railway," he said.
"The economics of what we are doing initially are very strong.
"As traffic builds up on this new railway line, I think we will see a case that is much stronger than it currently is for looking at further expansion."