Corbyn is considering entering the capital's 2024 mayoral race, according to the Mail on Sunday in a report that comes after a story in the Huffington Post in July said the former Labour leader's allies were urging him to run.
The 73-year-old had the parliamentary Labour whip suspended in 2020 for claiming the press and political opponents had "dramatically overstated" antisemitism under his leadership "for political reasons".
However, while no longer a Labour MP, Corbyn is still a Labour member.
So, it is unclear if the party would block an attempt by him to be its candidate, forcing him to stand as an independent.
Such a move would not be unprecedented. Former mayor Ken Livingston stood as an independent candidate and won in 2000 after being unsuccessful in his bid to be Labour's candidate.
Alistair Jones, associate politics professor at De Montfort University Leicester, said that should Corbyn enter the 2024 race as an independent, Labour voters could be split between him and current mayor Khan.
"The likelihood would be the Conservative candidate topping the first ballot (but not winning 50% of the vote). The question would then be how the anti-Conservative vote is re-allocated?
"Depending upon who comes second, will Labour voters back an independent Corbyn, or will Corbyn supporters vote Labour?
"Will non-Labour voters back either Labour or Corbyn? These are the great imponderables."
Khan, when asked if he was concerned about Corbyn entering the mayoral race, said he was "not surprised" that other people may have their eye on the job.
"One of the reasons I wanted to be the mayor was to give back to this city" Khan told Sky News on Monday.
"I won't be surprised if other people also expressed an interest – true or not."
It comes amid reports that Corbyn plans to run as an independent candidate in his constituency of Islington North in 2024, where he served as a Labour MP for almost 40 years.
Corbyn, who still canvassed for Labour in the local elections, told The Observer that he should have the Labour whip restored.
"I am honoured to be the full-time representative of Islington North, and to tackle all the issues facing our communities," he said.
"The whip was wrongly removed and it should be restored. Thousands of people in Islington North agree, as they repeatedly tell me in person."
However, according to The Guardian, senior Labour figures have said Corbyn would be "toxic" to winning back constituencies they lost in 2019 – warning he is "never getting back in" to the party.
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