Angela Rayner is reportedly considering a leadership challenge against Keir Starmer immediately after the local elections.
Supporters are said to be urging the former Deputy Prime Minister to turn against Sir Keir.
The local elections, which take place next Thursday, are understood to be make-or-break for the Prime Minister, as his premiership hangs in the balance.
Allies of Ms Rayner claim any delay would allow opposition candidates more time to lock in support among Labour MPs, the Times reports.
Wes Streeting, the Health Secretary, is widely seen as a favourite for the next Prime Minister.
Ms Rayner is currently under investigation by HM Revenue & Customs for her tax affairs.
Some polls show Labour could lose up to 2,000 seats.
It is understood the rumoured leadership challenge depends on the outcome of the votes.
Angela Rayner is reportedly considering a leadership challenge against Keir Starmer immediately after the local elections
|GETTY
If the former Deputy Prime Minister were to make a formal challenge, it would likely take the form of a speech, interview, or statement.
Insiders have claimed Ms Rayner was privately offered a return to Sir Keir Starmer's Cabinet in a final roll of the dice to stave off the potential leadership challenge.
Ms Rayner discussed her political future with Sir Keir during a visit to a school in Greater Manchester on April 14.
Other potential leadership candidates include Andy Burnham, the Mayor of Manchester, and Ed Miliband.
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| PAMr Burnham was present at the conversation between Sir Keir and Ms Rayner.
It is understood that Ms Rayner is hopeful that an HMRC investigation into her tax affairs will be closed as soon as this week.
Sir Keir managed to face down a leadership scare last night after 15 Labour MPs rebelled on a vote to investigate him over Lord Mandelson's appointment as the UK's Ambassador to the US.
The vote would have referred him to the privileges committee, the powerful Commons ethics body that forced Boris Johnson to resign.
When he was elected, Prime Minister Sir Keir Starmer appointed Angela Rayner as Deputy PM
| PAAfter the Prime Minister refused to rule out demoting Chancellor Rachel Reeves, Tory leader Kemi Badenoch said: "The former Deputy Prime Minister is on manoeuvres.
"This Government is like a bad episode of Game of Thrones. His own people have turned against him, and all the while, the Prime Minister is holed up in his castle, wetting himself about a visit from the King in the North yesterday.
"Mr Speaker, yesterday, one Labour MP actually said that his days are numbered."
Speaking on the potential cabinet reshuffle, Sir Keir's spokesman told the Times: "I don’t comment on reshuffle speculation. But you’ve got what the PM said before, that she’s hugely talented and he was really sad that he lost her."
A spokesman for Ms Rayner said: "Angela is focused on supporting Labour candidates ahead of these crucial elections."