EU officials have "significantly" increased the number of talks held with Labour since the snap election in June in which Ms May failed to win an outright majority, according to the Daily Telegraph.
Sources told the paper there had been a "significant change in tone" from Brussels since the result, with efforts being made to foster closer ties with Labour.
Negotiators reportedly fear that talks may be rendered completely useless if Ms May is ousted from office before their completion.
It follows Mr Corbyn's bold claims in June that Labour was a "government in waiting" and was ready to "take up the responsibility for Brexit negotiations."
In July, Labour held "very frank" talks with EU chief negotiator Michel Barnier lasting more than two hours.
The Prime Minister weathered fresh calls for her resignation this week following a disastrous speech at the Conservative party conference and claims more than 30 Tory MPs were plotting her demise.
Former party chairman Grant Shapps was denounced as the ringleader of the coup by loyalist MPs who rallied round in support of Ms May.
But the extra support for Ms May has done little to quash speculation that her premiership may be short lived.
Conservative MPs told The Independent there was no compelling reason to replace the Prime Minister for the time being, despite her conference disaster, but admitted her position remained perilous.
One former minister predicted, “Grant will fail”, but suggested the failed coup could accelerate a leadership bid by a more serious player.
The latest poll of who would make the best prime minister saw Mr Corbyn encroaching on Ms May's lead in the wake of her Manchester conference performance.
YouGov found she was still preferred over Mr Corbyn, by 36 per cent to 33 per cent - a three point lead down from eight points two weeks ago.