May's office declined to comment on a report in The Times newspaper that discussions on a timetable for the prime minister to stand down were now under way.
But a Downing Street source, speaking on condition of anonymity, told Reuters that the report was incorrect.
"News to me," the source said. "No, it's not correct."
The Times quoted an unidentified Downing Street source saying that even her closest allies believed it was inevitable she would have to resign.
The Daily Telegraph said that senior ministers had urged May to quit, and Buzzfeed reported that one lawmaker, a "whip" responsible for party discipline, had told her to set out plans to quit in the Sunday newspapers.
"She needs to set out a timetable for her departure and try to get her meaningful vote through. That's the best way forward," the Telegraph quoted an unnamed cabinet minister as saying.
Betting odds indicate there is now a 20 percent chance that May will be out of her job by the end of this month, Ladbrokes said on Saturday.
Brexit had been due to happen on March 29 before May secured a delay in talks with the European Union on Thursday.
Now a May 22 departure date will apply if parliament rallies behind the British prime minister next week. If it does not, Britain will have until April 12 to offer a new plan or decide to leave the European Union without a treaty.
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