Jeremy Corbyn will "listen to Labour members" and support a soft Brexit, according to Labour MP Liz Kendall.
Corbyn does not share the pro-European attitude of the majority of Labour voters and has so far declined to soften the party's stance on the issue.
However, Kendall, a former Labour leadership candidate, suggested Corbyn will soon change his mind.
The former shadow Cabinet member added Labour needed to offer a clear alternative to the Conservatives on Brexit.
"I know the leadership is very concerned with being a democratic party and I believe they will listen to the members on this," Kendall said in an interview with Business Insider.
"We have already rightly said that Britain should remain in the single market and customs union during the so-called transition. I believe that we'll end up going further because we have to have a clear alternative to the Conservatives."
Labour's policy so far has been that Britain should leave the European Union after Brexit, but it should remain in the single market and customs union during the transitional period. Last month Corbyn reiterated the UK could not remain in the single market once it leaves the bloc.
The comments left a number of pro-European Labour MPs dismayed, particularly as a survey released a few weeks earlier showed 87% of Labour voters wanted to stay in the single market and customs union according to a recent poll.
Last weekend, the Labour leader ruled out holding a second Brexit referendum, despite the fact deputy leader Tom Watson had previously expressed himself in favour of one.
"We are not asking for a second referendum," Corbyn told Andrew Marr over the weekend.
However, Kendall hinted a vote on the terms of the deal was a lot likelier than it was a few months ago.
"The possibility of it is now on the agenda like it wasn't a few months ago," she said.
"I think there are real issues with referendums. Like seeing Nigel Farage and cronies pile in with lies and information like £350m for the NHS on the side of a bus.
"But the principles of there being a final say — whether that being in Parliament, where it must happen, or in the country — is more of a possibility than we've seen before."