Labour's mayoral candidate has hinted she might be ready to step aside to let Ken Livingstone take over the role.
Mr Livingstone was expelled for running as an independent in 2000
Labour's ruling board is expected to decide next week whether to readmit Mr Livingstone to the party early.
In a statement, Labour candidate Nicky Gavron said the best way to reunite the party's vote in London was to combine the strengths of both their campaigns.
Mr Livingstone was expelled for five years for running against Labour in the 2000 mayoral poll.
Labour's London regional board is tipped to discuss Mr Livingstone's position when it meets on Monday, ahead of the party's National Executive Committee meeting on Tuesday.
The London mayor told BBC Radio 4's Today programme: "I hope it's all going to be resolved by Wednesday."
Earlier, Ms Gavron said: "During the last few months I have listened
intently to the views and concerns of party members and supporters at every
"My absolute priority is to reunite the Labour vote in London.
"The best way
to achieve this unity is to combine the existing strengths of both our campaigns
and for Ken Livingstone and myself to work together for the good of Labour and
Ms Gavron's words were welcomed by Paul Kenny, London regional secretary of the GMB union, who said his members would be delighted by the news.
"Ken has followed progressive policies on transport and affordable housing, as well as campaigning to improve the lot of low paid public sector workers," he added.
Prime Minister Tony Blair is thought to want Mr Livingstone back into the Labour fold amid fears otherwise Labour's official candidate could be pushed into fourth place in next year's election.
But Chancellor Gordon Brown and Deputy Prime Minister John Prescott are among other ministers believed to be opposed to the move.
Asked what he made of the latest reports that Mr Livingstone was to be let back into Labour, Mr Brown told Today: "That is a matter for the National Executive Committee of the Labour Party. It is not a matter for the cabinet.
"That will be their decision, not mine."
Mr Brown has said he wanted to be appointed to the NEC but his request was blocked by the prime minister.