Starmer has already removed deputy leader Angela Rayner as party chair and campaigns coordinator, after Labour lost control of a host of councils and the “red wall” parliamentary seat of Hartlepool for the first time since its inception in the 1970s.
The Labour leader has faced a backlash from senior figures for apparently sacking Rayner.
Allies insist she has been offered another job in the shadow cabinet but they could not say what it would be, with Starmer in the process of reshuffling his top team on Sunday.
Reports suggest shadow communities secretary Steve Reed could be in line to replace Rayner.
Ian Murray, the shadow secretary for Scotland, and MP Chris Bryant have also been tipped for promotion.
Shadow chancellor Anneliese Dodds is meanwhile among those reported to be in line for a demotion.
There has also been criticism from some sections of the party of Starmer’s key aide Jenny Chapman, the former MP for Darlington.
Speaking to Times Radio on Sunday, Murray insisted Rayner had not been sacked and that Starmer wants to move her to a “much more prominent role” so Labour can benefit from her “authentic voice”.
But after headlines that Rayner had been sacked sparked outrage from some in the party, Murray admitted: “Communications over the last 24 hours have not been top-quality.”
Greater Manchester mayor Andy Burnham, who has signalled he is ready to take over from Starmer if asked, said of Rayner’s sacking: “I can’t support this.
“This is straightforwardly wrong if it’s true.”
Members of former leader Jeremy Corbyn’s team, who come from the left of the party, were among those to criticise the move to “scapegoat” the deputy leader.
Former shadow home secretary Diane Abbott called it “baffling” while John McDonnell labelled it a “huge mistake”.
McDonnell, a former shadow chancellor, told the BBC’s Andrew Marr Show: “When the leader of the party on Friday said he takes responsibility for the election result in Hartlepool in particular and then scapegoats Angela Rayner, I think many of us feel that is unfair, particularly as we all know actually that Keir’s style of leadership is that his office controls everything.
“It is very centralised and he controlled the campaign.”
In a further sign of the splits in the party, Labour grandee Lord Peter Mandelson urged Starmer to dilute the influence of party members and “hard left factions” linked to train unions.
He said Starmer was set to embark on a “serious review” of Labour policy.
“I also believe that he needs to to look at how the party is organised, how it represents the genuine grassroots of the party and reflects the genuine views and values of Labour voters across the country in all the nations and the regions of the country,” Mandelson told Times Radio
“The idea that the Labour Party and its policies and its outlook can be driven disproportionately frankly by a mixture of grassroots members in London and the south-east and the sort of hard left factions that are attached to trade unions - that has got to go, we have got to change.
“Party reform therefore I think is an essential part of what Keir has got to take on next.”
As well as undertaking a reshuffle, Starmer has hired Gordon Brown’s former chief pollster Deborah Mattinson – who has written a book about why Labour lost the so-called “red wall” at the 2019 general election – as director of strategy.
This article originally appeared on HuffPost UK and has been updated.