Talks between the UK and the EU on a post-Brexit trade agreement continued during the night, but a deal is expected to be unveiled on Thursday.
Negotiators in Brussels are said to be trying to finalise details on fishing quotas, which have proved an obstacle to an agreement during months of talks.
The PM has briefed his cabinet.
Boris Johnson is expected to speak to European Commission President Ursula von der Leyen on the phone, BBC political editor Laura Kuenssberg said.
A press conference is then expected to follow.
Laura Kuenssberg said she understands there were four calls between the pair to get a Brexit deal “over the line” – and the final one is “expected to sign and seal”.
Amid speculation that both sides were close to unveiling a deal on Wednesday evening, European Commission spokesman Eric Mamer tweeted just after midnight GMT to confirm the talks would be continuing.
“Work will continue throughout the night. Grabbing some sleep is recommended to all Brexit-watchers at this point,” he said.
“It will hopefully be an early start tomorrow morning…”
The deal document is thought to be around 2,000 pages long, with both sides having until 31 December – when the UK leaves EU trading rules – to get it approved by parliamentarians.
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A deal would end the prospect of the two sides imposing widespread import taxes – tariffs – on each other’s goods from 1 January, which could have affected prices.
EU sources said Mr Johnson and Mrs von der Leyen had been in contact in recent days an attempt to break the deadlock before an expected pause in negotiations for Christmas.