Andy Burnham has signalled he does not want to discuss the prospect of a second independence referendum with First Minister John Swinney during his visit to Scotland.
The two leaders are set to convene on Thursday, marking their first face-to-face meeting since Mr Burnham became Prime Minister on Monday.
Their meeting follows a phone call between the two earlier in the week, during which Mr Burnham reportedly dismissed the prospect of another independence vote.
A UK Government source indicated the Prime Minister told the First Minister they would have to "agree to disagree" on the matter.
Despite this divergence, Mr Burnham, who has expressed a desire to devolve more powers across the UK, is understood to have committed to collaborating with the Scottish Government to foster a "new kind of politics".
However, Mr Swinney has already indicated his reluctance to work with Scottish Secretary Douglas Alexander, a figure Mr Burnham chose to retain in his cabinet.
The First Minister said he would rather deal with the Prime Minister one-on-one, having accused Mr Alexander of souring relations between the UK and Scottish governments.
The UK Government has said Mr Burnham would set out how he plans to work “collaboratively” with devolved governments “based on a genuine partnership”.
The Prime Minister said: “When I say we need good growth in every postcode, I mean every postcode across the whole of the UK. Every place and every person matters.
“I’m not focused on point scoring or discussing constitutional changes like referendums, I want practical measures to help people live well and bring back hope.
“That’s why I’m giving families more breathing space with help on the cost of living, which I have started this week by taking VAT off electricity bills, saving money for millions of households.”
Mr Burnham will arrive in Glasgow on Thursday to watch the opening ceremony for the 2026 Commonwealth Games, where he will be joined by the King and Queen.
He will also meet the First Minister of Wales, Rhun ap Iorwerth.
He said: “I look forward to meeting the Prime Minister in Glasgow today.
“It is fitting that we meet in Scotland, as it underlines Wales’ case for parity of powers and a fairer funding model that reflects our needs.
“‘Number 10 North’ must not become just Whitehall with a different postcode. I agree wholeheartedly on empowering communities – it’s at the heart of my politics – but decisions affecting Wales should be made in Wales, and it is for the Welsh Government and our Senedd to work with the people of Wales on how power is exercised and shared within our nation.
“At a time when families are still feeling the pressure of the cost of living, I am also keen to discuss how our governments can work together as equal partners to deliver improvements to the lives of people in Wales.”
Mr Burnham’s visit to Scotland marks a change from his successor, with Sir Keir Starmer choosing not to campaign in Scotland for the Holyrood election.
Scottish Labour figures have pointed to Sir Keir as the reason for the party’s Holyrood election results in May – its worst in the history of devolution.
Mr Burnham is poised to make Scottish Labour leader Anas Sarwar a minister, a move that will see him leave the Scottish Parliament and head to the House of Lords.
The PM is also expected to meet with the First Minister and Deputy First Minister of Northern Ireland on his tour of the UK in August, where he will visit areas across Scotland, Northern Ireland, Wales and England.
