A timetable for elections to find a new leader when Tony Blair quits is expected to be agreed next week by Labour's National Executive Committee.
Two MPs have so far declared their intention to run for Mr Blair's job
Mr Blair is expected to announce his retirement as prime minister after the Scottish and Welsh elections on 3 May.
There will then be a seven-week contest for the position of Labour leader and deputy leader, the BBC understands.
Gordon Brown may still be required to attend hustings and face a vote even if he is the only leadership candidate.
So far two candidates from the left of the party, Michael Meacher and John McDonnell, have declared their intention to challenge Mr Brown for the top job.
But it is not certain that they will be able to gain the 44 signatures of other Labour MPs needed to get on to the ballot.
Mr Brown, who has been criticised by some for not spelling out his plans for when he becomes leader, told the Financial Times on Friday: "As and when there is a leadership election for the Labour Party, I will set out what I intend to do."
Mr Blair has said he intends to attend the G8 summit in Germany from 6 to 8 June.
If he were to resign on the day after the Scottish and Welsh elections, Britain could have a new prime minister by Friday, 22 June.
But the Labour Party would have to call a special conference to announce the new leader, which is more likely to be held at a weekend.
The first week of the seven-week leadership campaign would cover the nomination period, when all candidates would be required to show they had support of at least 44 other MPs.
That would be followed by six weeks of campaigning, with voting among MPs, party members and unions taking place over the final three weeks.
The party wants to hold five hustings around the country, to give party members a chance to question the contenders, the BBC understands.
BBC political correspondent James Hardy said that - if no-one gains enough support to run against Mr Brown for the leadership - there is a strong possibility he will still be required to attend these hustings along with the deputy leadership candidates.
Labour backbencher Andrew MacKinlay expressed concern that the rules were being adapted to ensure Mr Blair could attend the EU and G8 summits in June.
He said if Mr Brown was the sole nominee, he should be declared the winner.
"It seems of no purpose to go through this hustings charade when there's no mechanism for what would happen if the sole candidate was rejected at the end of it," he said.
Six MPs have confirmed they will run for the deputy leader's job, to replace John Prescott who has said he will stand down with Mr Blair.
The contenders include five cabinet ministers - Peter Hain, Hilary Benn, Harriet Harman, Hazel Blears, Alan Johnson - and one backbencher, Jon Cruddas.
But former minister John Spellar questioned whether the Labour Party, which has debts of about £23m, should hold a deputy leadership election at all - when the Conservatives and the Lib Dems did not.
He added that the contest meant fellow ministers had to "differentiate themselves from their colleagues, rather than hold to collective responsibility" adding: "It's not a recipe for good government."