Mr Corbyn said his party was not seeking a new Brexit vote at the moment but failed to explain whether they would in the future.
Talks of a second Brexit referendum were reignited when pro-Brexit politician Nigel Farage suggested a new vote could “silence” Remainers.
The Labour leader said: “We are not supporting or calling for a second referendum. What we’ve called for is a meaningful vote in Parliament and that is the one area that I think Parliament has asserted itself in the vote before Christmas.”
But when asked about Labour’s stance could change in the future Mr Corbyn failed to deliver a clear response.
Mr Corbyn however appeared to finally settle on whether his party would call on the British Government to stay in the single market, saying Britain cannot remain a member of the single market because of its decision to leave the European Union.
Speaking on Peston on Sunday, he continued: “The single market is dependent on membership of the European Union.
“Do we have a trading relationship with Europe which is tariff-free, which is based on access to that market, and access of Europe to our market? Yes. “Do we push for that in the negotiations? Yes. Is that what we have said to the European Union in opposition? Yes.
“You have to make a special relationship with the European Union.”
Single market membership after Brexit has become a divisive issue within Labour, with members struggling to reach a common party line on the matter.
And divisions are set to continue as Mr Corbyn‘s comments were met with criticism by several MPs.
Nottingham East MP Chris Leslie responded on Twitter, seemingly rejecting Mr Corbyn’s statement by posting four times: “The Single Market is NOT dependent on membership of the EU #worthrepeating.”
Pro-Remain Labour Chuka Umunna also questioned the statement, pointing out countries like Norway and Iceland maintained access to the single market despite being outside the European Union.