Sir Keir Starmer has said the UK should pursue closer alignment with EU markets "if it's in our national interest".
Speaking to the BBC's Laura Kuenssberg, the prime minister said it would be "better looking to the single market rather than the customs union for our further alignment", to avoid jeopardising trade deals with the US and India.
But he insisted the government would not reverse its manifesto pledges to stay out of the EU single market or customs union, or to end freedom of movement.
The comments are Starmer's clearest indication yet that he wants to pursue a closer relationship with Europe in a broader number of areas.
He said: "I think we should get closer, and if it's in our national interest to have even closer alignment with the single market, then we should consider that, we should go that far.
"I think it's in our national interest to go further."
He added: "I actually think that now we've done deals with the US, which are in our national interest, now we've done deals with India which are in our national interest, we are better looking to the single market rather than the customs union for our further alignment. And it wouldn't be in our interest now to give up."