Tom Watson has cast doubt on whether he will ever become deputy prime minister as he appeared to leave the door open to a second EU referendum.

Labour’s deputy leader said he had “no idea” if Jeremy Corbyn would appoint him as number two if the veteran socialist makes it into Downing Street and suggested the role could be handed to Emily Thornberry.

Watson also declined to reject the prospect of Labour offering a second referendum when he told the BBC’s Pienaar’s Politics “you shouldn’t rule anything out”.

He spoke out yesterday as Theresa May’s hold on her job seemed to strengthen following positive briefings into Sunday newspapers from Tory MPs following her deal with EU leaders.

Watson said Labour had argued that it did not wanted power to be taken from Brussels and given to “the executive or unelected bureaucrats in Whitehall”.

“We’ve not said we want a second referendum, what we actually want is a negotiated settlement.”

When pressed on whether Labour would rule out a second vote, he said: “When you’re in complex negotiations on behalf of the nation you shouldn’t rule anything out. What I am trying to say to you, I don’t think it is likely at all, it would be more likely that we try and renegotiate the deal should parliament reject it.”

Watson also prompted intense debate among activists when he played down the prospect of his becoming deputy prime minister.

Corbyn has been urged to create the post of a second deputy leader, to allow him to appoint a woman, and improve gender balance in his top team. Thornberry, the shadow foreign secretary and Corbyn’s Islington neighbour, has been touted as one person who could fill the job.

When Watson was asked if he would become deputy prime minister, he responded: “I have no idea whether that will ever come to pass and I probably doubt it.”

He then added, to laughter from other BBC guests: “I think he [Corbyn] would probably give it to Emily Thornberry if I’m being honest – there’s no hard feelings about that Emily.

“If you are really asking me is ‘do I think Labour can win the next election, whenever that happens? I think yes.

“I think that election could come sooner rather than later – it feels to me like there is still instability at the heart of Theresa May’s government. It could implode on itself at any point and that puts under pressure because obviously we have got to be in preparation for a potential early general election.”