The Labour leader revealed that he has not talked to his predecessor since a damning Equality and Human Rights Commission (EHRC) report into antisemitism in the party was published last October.
Mr Corbyn’s dismissive response to the report saw him suspended from Labour. Although he was allowed back as a member, he still sits in parliament as an independent MP.
“He’s not got the whip at the moment – so he’ll be able to run but wouldn’t be able to as a Labour MP,” Sir Keir told BBC’s Political Thinking podcast.
Asked if he thought this was likely to remain the case going into the next election, the Labour leader said: “I don’t know. But at the moment that may be the case.”
Sir Keir also said Mr Corbyn “knows” how to be reinstated as a Labour MP. “It’s up to him. He knows what he must do to move this forward. He’s not chosen to do so – that’s his choice.”
Mr Corbyn claimed that the scale of antisemitism inside Labour had been “dramatically overstated for political reasons” by his opponents following the highly-critical October 2020 report from the EHRC into the party’s handling of complaints under his leadership.
The left-winger was later readmitted as a member by the party’s NEC after he backtracked and admitted that concerns about antisemitism were neither “exaggerated nor overstated” – but the whip was withheld.
Sir Keir claimed Mr Corbyn’s remarks had undermined “our work in restoring trust” and has suggested he would have to issue a fulsome apology for his remarks before he could be reinstated.
It comes as Tony Blair has urged Labour to “emphatically reject” so-called woke-ism and push its far-left factions “to the margins” if it is to defeat the Conservatives and win power again.
The former prime minister’s call comes in a foreword to a report suggesting Labour will need a larger voter swing to win the next election than was seen during Mr Blair’s landslide victory in 1997.
The party’s former leader said that a “lurch to the far left … will never be electorally successful” following the party’s defeats at the 1983 and 2019 elections – and urged Starmer to continue to bring the party back to the middle ground.
Mr Blair argued the party still has a “culture problem with many working class voters” as well as a “credibility problem” with those in the centre of the political spectrum.