Liberal Democrat leader Sir Vince Cable said agreeing to a confirmatory referendum on the deal could secure the Commons majority Mrs May needs for her Withdrawal Agreement following three previous failures to get it approved.
In a letter to the Prime Minister, he said a referendum presents an “alternative way forward”.
Sir Vince said: “A Withdrawal Agreement which has been declared dead could be resuscitated at the last moment, and would have some chance of being endorsed by the public.”
He called on Mrs May to convene a meeting of opposition party leaders in support of a referendum to agree on an approach which could secure a majority for the Brexit deal.
He added: “Providing Jeremy Corbyn sticks to his party policy, you could achieve a majority akin to that which was obtained for triggering Article 50.”