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The prime minister has ruled out handing powers to hold a referendum on independence to the Welsh government.
Andy Burnham said other UK nations do not have such powers and he did not "think we can create a different arrangement for Wales".
He added that the decision should be made jointly with Westminster, arguing that the UK Parliament has to have a "say on an issue of that magnitude".
Wales First Minister Rhun ap Iorwerth said last week he would seek powers to hold an independence referendum, although he ruled out staging one before the next Senedd election in May 2030.
Burnham also said he was open to looking at the Welsh government's "Cynnal" plans to trial offering £10 a week for 15,000 children aged under six, in households already receiving universal credit.
This would require the agreement of the Department for Work and Pensions and HMRC to avoid the payment being taxed or other benefits - paid for by the UK government - being reduced.
"I'll certainly ensure that there's a proper discussion about the issue," he said.
"I mean, I did things as mayor of Greater Manchester without there having to be any tax implications.
"So I'm not quite sure why that arises in this in this instance, but we will have a look at it for certain."
During a visit to the Tata steelworks in Port Talbot in August, Burnham indicated he was "open" to the idea of giving the Welsh government control over policing.
BBC Wales understands that idea faces oppostion from many Welsh Labour MPs, with one calling it "a travesty".
In response Burnham said on Friday it was "about looking at the case" rather than taking "a fixed view".
He added: "I just need to look at it on the merits of the case. I'm the prime minister of all of the UK, including Wales.
"I have to respect the governments in the the nations of the UK, and I will, and give fair hearing to anything that is is put to me."
