Sir Keir Starmer met Andy Burnham for talks earlier on Tuesday, as he seeks to ensure an "orderly" transition of power after announcing he is standing down as prime minister.
It is the first time the pair have met since Burnham won last week's Makerfield by-election.
The hour-long meeting, which was first reported in The Times, comes as Sir Keir authorised access talks with civil servants for prospective Labour leadership candidates to prepare them for government.
Burnham is the only candidate to have emerged so far and if he does not face a challenger he could become prime minister as early as 17 July.
The PM's spokesman said the access talks will begin "as soon as possible" and before formal nominations for any Labour leadership contest close on 16 July.
The talks will focus on the "formation of government and key policy priorities", the PM's spokesman added, and would include security briefings.
He said he did not know if Burnham had formally requested access talks, adding that the decision to make them available had only just been made.
It comes after Sir Keir announced he would be standing down as prime minister after less than two years, after losing the support of Labour MPs.
Speaking at a cabinet meeting on Tuesday morning, Sir Keir said he wanted whoever became the next prime minister to succeed, his spokesman said.
The PM added that he would "seek to resolve difficult issues in the coming weeks to support his successor" and " seek to make the transition as easy as possible".
Sir Keir has agreed to suspend "major policy" and spending decisions until a new PM is in place.
Andy Burnham has yet to set out a detailed policy agenda or indicate who would get the top jobs - including chancellor - in a government headed by him.
He is due to make a series of speeches aimed at demonstrating a shift in approach from Sir Keir, starting next week with one on devolution and the economy.
The former Greater Manchester mayor, who returned to Parliament this week after winning the Makerfield by-election, has committed to Chancellor Rachel Reeves' fiscal rules, in a sign he would not oversee a big rise in government borrowing.
He has also committed to Labour's manifesto promise not to increase the main rates of income tax, VAT or National Insurance, which would limit his ability to raise significant sums from tax.
But he has spoken about the need for more public control over utilities like water, building more council houses and "reindustrialising" the economy, among other priorities.
Cabinet minister Darren Jones and former armed forces minister Al Carns are being considered as potential candidates by some Labour MPs worried about installing Burnham in No 10 without a contest.
But it is not clear whether they will gather enough support to get on the ballot paper.
Jones said he was not currently minded to run but that he would want assurances on the former mayor's approach to economic policy, amid concerns among some potential unease in the markets.
