Speaking on the BBC’s Good Morning Scotland, Ian Murray, the MP for Edinburgh South, said he believed a call for a second referendum - or People’s Vote - could command a majority in the House of Commons if supported by the Labour frontbench.
Other opposition parties have been pressing Mr Corbyn to call a motion of no confidence in Theresa May’s Government. Labour, as the official opposition at Westminster, is the only party able to do so.
However, the Labour leader has ruled out the move, which could trigger a general election, until he can be sure of winning the vote.
Mr Murray said: “The Labour Party will have to come off the fence on that at some point pretty soon because I think what they’re trying to do might be incompatible with what’s available.
“There’s a majority of MPs that would stop a no-deal scenario from happening so that could be taken off the table.
“I think we can get a majority around a People’s Vote because we need to try and break the impasse between now and the 29th of March.”
Mr Murray said that cross-party talks in Parliament are ongoing to try and push for another EU vote.
Mr Murray said: “There’s a growing number of Conservative backbenchers, and it’s not just the usual people that are doing this in terms of supporting a People’s Vote - we’ve got Guto Bebb who’s supporting it, Jo Johnson’s come on board recently. There’s a growing number of Conservative MPs.
“So we do need to get the Labour frontbench into a position of a People’s Vote and if we can do that, I think we can command a majority in the House and I think that’s the best way to go.
“We’ve got to ask ourselves why we came into politics. I didn’t come into politics to make my constituents and the country poorer.
“And therefore, given what’s on the table is the worst of all worlds and given there’s an impasse in Parliament, the public should be brought back into this process democratically.”