
In response ap Iorwerth said: "This is not a great start even before he starts in the job.
"It does not give me an awful lot of confidence in seeing something that is rather important to Wales being somehow cast aside before Andy Burnham even gets the chance to become prime minister.
"There are real issues that we are facing in Wales, and I am hoping that Andy Burnham's experience of working in a devolved context in Manchester would help him to understand what those issues are."
He added that Burnham should not "duck out of" dealing with funding and repeated his calls for more powers over borrowing and taxation to be given to the Welsh government as well as devolution of rail, policing, justice and the Crown Estate.
Ap Iorwerth said the two men are yet to speak, but that it would need to happen "very soon" if Mr Burnham takes over in Downing Street.
Additional UK government funding for Wales is calculated using the Barnett Formula.
It determines the amount of cash the Welsh government receives, based mainly on share of population.
Critics have long argued that it underfunds Wales, despite Wales receiving more funding per head than England, because the Welsh population is relatively older and more infirm.
An overhaul of the funding formula is also backed by Welsh Labour.
Less than a year ago the Welsh Labour conference passed a motion calling for reform, a call that was rejected two months later by Chancellor Rachel Reeves.
A major assessment of Wales' needs was last carried out by the economist Gerry Holtham in 2010.
Burnham co-wrote a book with his Liverpool counterpart Steve Rotheram when he was mayor of Greater Manchester in 2024, which outlined how they would tackle inequality and overhaul the distribution of public money.
In it they wrote that a "new formula covering the whole of the UK and including the English regions as separate entities" was needed, and that funding "would be allocated to the regions and nations based on social factors and levels of need".
The book also compared the UK to a "rambling stately home" in which the power was only on in some rooms.
He likened the "main living room" where the lights worked well to Greater London, said that Scotland was the main bedroom where the "lights flicker" and that: "down end of the landing, there are two smaller bedrooms where the lights work but are much dimmer. I think you know where this is going – they are Wales and Northern Ireland".
The pair also proposed scrapping the Treasury's "Green Book" - the official UK government spending guidelines.
Critics argue that it disadvantages Wales and the English regions by channelling investment to the south east of England.
During his 2015 bid for the Labour leadership, Burnham said he had known Wales received an unfairly low share of UK spending when he had been a Treasury minister eight years earlier.
He told BBC Wales he had been unable to change government policy but "I believe Wales has been short-changed and as leader I would take steps to correct that".
Burnham, who has returned to the House of Commons after winning the Makerfield by-election last week, is so far the only contender to replace Sir Keir Starmer.
Starmer announced his resignation on Monday and Burnham could be prime minister as early as 17 July if no other challenger emerges.
The UK government's Wales Office minister, Bangor Aberconwy MP Claire Hughes, was asked by BBC Radio Wales Breakfast what a Burnham premiership would mean for Wales.
She said it was "early days" but there was "genuine excitement" about reports in the Financial Times that his plans include "relocating some of the Number 10" operation to Manchester.
But she said it was "up to Andy Burnham to set out his policy platform and his thoughts around devolution for Wales when, [and] if, he becomes prime minister".

