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.
Access talks are normally granted to opposition party leaders ahead of a general election.
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.