The UK should "explore" allowing qualified free movement of workers from the EU after Brexit, Shadow Brexit Secretary Sir Keir Starmer has said.
In a potential softening of Labour's position, Sir Keir called for alignment with the EU's single market.
This could pave the way for EU migrants with jobs to be allowed to settle in the UK, subject to certain conditions and for Britain to accept EU rules restricting state aid.
The shadow cabinet minister made his remarks in an interview with Newsnight during a visit to Belfast after meeting nationalist parties.
He said Labour hoped to negotiate a future relationship with the EU involving a "comprehensive customs union and single market alignment".
This would avoid the need for a backstop, by guaranteeing no hard border in Northern Ireland.
'Most people would accept that'
Asked whether he could live with the Norway Plus plan, which would involve free movement of workers, Sir Keir said: "Well that would have to be explored and the precise detail of that."
The Norway Plus or the Common Market 2.0 plan - promoted by Labour MP Lucy Powell and Tory MP Nick Boles - would involve membership of a customs union and the free movement of workers, rather than EU rules allowing free movement of citizens.
Sir Keir said people would be willing to accept the movement of workers subject to restrictions: "If somebody is coming to do a job and it needs to be done and it has been advertised locally beforehand with nobody able to do it, then most people would say I accept that."
"Most people say that if you are coming to join your family that is something I can accept. Most people would say if somebody wants to come here and study and it is genuine then of course please come and study. In fact let's celebrate that," he added.
"So I actually think we get stuck on the freedom of movement discussion too early without saying what does a principled, effective and fair immigration policy look like?
"When we get into that debate we may find we can make better progress than we think."
Prime Minister Theresa May has maintained that free movement will end when the UK leaves the EU.
Sir Keir described free movement as one of two areas - along with staying aligned with the rules of the single market - that would be "sticking points" in negotiations with the EU under his plan.
"There is a negotiation to be had there. But I genuinely think that if 12, 18 months ago we had been clear, as the UK, to say we want a close economic relationship, we want these features - customs union, single market alignment - and the only sticking points now were how exactly do you stay aligned, what is the proposition about freedom of movement but we know what we are trying to achieve - we would be in a materially better place than we are now."
Sir Keir said he did not believe that EU state aid rules would be a problem because they do not "cut across" Labour's 2017 election manifesto.
He also said Labour would have no problems with observing a common playing field with the EU and upholding workplace and environmental rights that keep pace with EU.
Sinn Fein and the SDLP were alarmed last week when Jeremy Corbyn expressed unease at the Northern Ireland backstop which is strongly supported by nationalists.
The backstop is designed to avoid a hard border by tying Northern Ireland closely to the EU, if the UK and Brussels fail to agree a future relationship before the end of a 21-month transition period.
SDLP leader Colum Eastwood told Newsnight that Mr Corbyn was in danger of echoing the language of the DUP after the Labour leader warned that Britain could be tied into the backstop indefinitely.
Sir Keir reassured Sinn Fein and the SDLP that Labour remains committed to the backstop, as long as Theresa May maintains her red lines.