The Labour leader dismissed suggestions he was "staunchly against" one of the key principles of the European Union – the ability to live and work freely in the 28 member states.
At the 2017 snap election, Labour's manifesto said "freedom of movement will end" when Britain exits the bloc, but today Mr Corbyn appeared to soften this stance.
In an interview, Mr Corbyn also said his party does not currently support Theresa May's Withdrawal Agreement Bill without any fundamental changes as the prime minister braces for yet another defeat in the Commons.
And he appeared to give a warmer endorsement of a Final Say referendum, but Labour sources played down Mr Corbyn's comments claiming there was no shift in policy.
Pressed on the issue of free movement, Mr Corbyn the BBC's Andrew Marr Show: "I'm not staunchly against freedom of movement. Our manifesto said the European system would not apply if you're not in the European Union – but I quite clearly recognise there has to be a lot of movement of workers.
"Ask any company in manufacturing or any other sector how much they need and rely on workers from Europe and indeed the other way around."
Told there are countries outside the EU that have chosen to retain free movement, Mr Corbyn said: "That would be part of our negotiations with the EU."
He added: "Part of our negotiations, the extent to which workers would transfer from one country to the other and what the needs for it would be."
Asked if Labour would keep free movement as a non-member of the EU, Mr Corbyn replied: "It would be open for negotiation the level of movement of people between Europe and this country if we're a non-member of the EU."
He was also repeatedly pressed for clarity on Labour's Brexit stance ahead of the European elections this week – and interviewer Andrew Marr presented Mr Cobryn with a series of conflicting views from members of the shadow cabinet.
Asked if the Labour election slogan was "Vote Labour, get Brexit", Mr Corbyn said: "I think what would be a fair assessment would be to say Vote Labour, challenge austerity and guarantee living standards for the future, not a no-deal exit from the European Union which is all that's being offered by the Tory right and, in a sense, by the Tory party."
Mr Corbyn reiterated a second referendum should be an option on the table to respond to what emerges from parliament, although added MPs have yet to reach agreement.
He was also pushed on what he meant when saying "option", to which he replied: "We would want a vote in order to decide what the future would be, so yes."
Asked if a second referendum would be disastrous, Mr Corbyn replied: "No, I don't think anything like that is disastrous but I think it has to be an opportunity for public debate and public discussion, but it has to be about something and that's why I have made the point clear about a customs union and trade and rights protection."