The no-confidence vote may be announced by the backbench 1922 Committee of the UK Parliament's House of Commons, which should receive 48 letters in favour of the motion from Conservative lawmakers. Most of the letters have already been submitted, according to local media reports.
Earlier, the UK prime minister responded to reports about the idea of extending the transition period until the end of 2022 that allegedly was suggested by EU Chief Negotiator for Brexit Michel Barnier.
"I think it is important that in delivering for the British people we are out of the implementation period before the next general election," May said at the annual conference of a UK business organization, the Confederation of British Industry.
Under the latest draft deal, the transition period is expected to last until the end of 2020 with a one-time extension possibility. The duration of the extension remains to be agreed.
The reports come after May defended a draft Brexit deal in the House of Commons on November 15. The agreement faced criticism both from the opposition and from the ruling party, with several members of May's cabinet having resigned over their disagreement with the deal.