Pollsters have predicted Labour will suffer losses across the country in the local elections on May 4th, with the Conservatives and Liberal Democrats poised to make significant gains in England and Wales.
It has also been predicted Labour may fail to retain any local authorities in Scotland, with the SNP and Scottish Conservatives set to capitalise on strong opinion polls.
Mr Foster wrote: “If the results are as bad as predicted, then Jeremy should stand down voluntarily and let someone else lead the fight in June.
“If he does not – and I don’t believe he ever would – I would be very happy to fight him and his fellow travellers on the extreme left of the party by standing in his constituency of Islington North.”
Mr Corbyn has been Islington North MP since 1983, winning the seat in 2015 by more than 21,000 votes.
Mr Foster, one of the party’s largest donors, was suspended from the party last year after penning an inflammatory article in the Mail on Sunday in which he compared supporters of Mr Corbyn to Nazi stormtroopers.
Earlier that year Mr Foster lost a High Court battle to prevent Mr Corbyn from running in the Labour leadership contest.
Shadow chancellor John McDonnell called for action to be taken against Mr Foster, saying his comments were “appalling”.