Angela Rayner is being positioned as a "credible" alternative to Sir Keir Starmer as the Prime Minister faces concerns about a backlash from his own backbenchers.
Allies of the Deputy Prime Minister say she knows she needs to distance herself from Starmer, with one Rayner ally saying she did not want the "blood" of unpopular policies on her hands.
Those close to Rayner have denied the news is related to the leak of an internal government memo in which she insisted Chancellor Rachel Reeves should raise taxes rather than reduce spending.
The memo suggested limiting migrants’ access to the state pension and increasing the NHS surcharge that people with visas must pay to cover potential health treatment.
Deputy Prime Minister Angela Rayner is being positioned as a 'credible' alternative to Keir Starmer
PAOne source told The Times: "Angela has been loyal in public but she knows she needs to distance herself from some of the unpopular policies.
"Starmer is not under any kind of threat now but if things have not improved closer to the next election that could change.
"Angela is ambitious and she needs to be credible if she is to present herself as the candidate of the left. This is something people are talking about."
Another added: "Angela has significant backing not only within the [parliamentary Labour Party] but also among Labour members, and she would undoubtedly win a leadership contest if there was a vacancy.
"It’s a strategic oversight by No10 not to tap into her experience, expertise and insights."
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Deputy Prime Minister Angela Rayner talks with Health Secretary Wes Streeting
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A government spokesman told The Times: "We don’t comment on leaks."
It comes as speculation about Rayner's potential ambition to rise to the top of the party have been waved away by allies.
However, they suggested the MP for Ashton-under-Lyne could challenge for the role if Health Secretary Wes Streeting were to theoretically stand unopposed.
One told The Telegraph: "I don’t think she wants it. The invasion of her private life was uncomfortable... But if no one else emerges to take on Wes, then she would do it."
Despite the speculation, senior Labour MPs have been quick to talk up the unity within the cabinet.
Asked about the memo by the BBC, the environment secretary, Steve Reed, said the cabinet was "united behind the government’s plan for change."
An unimpressed senior Labour MP also told The Telegraph: "I think they were poor policy suggestions and demonstrated how hard it is to raise not all that much."
