The prime minister also called for an end to “tribal politics” between the Scottish and UK governments.
He said he and Swinney “agreed on some things” but “didn’t have to agree on everything”.
Swinney is expected to promote his renewed push for independence in his keynote speech at the SNP conference on Saturday.
He previously welcomed Burnham telling MPs that a border poll would be considered in both Scotland and Northern Ireland if there was a clear consensus and public opinion had changed.
But Burnham later pushed back on that by telling Swinney at a meeting in Glasgow that a second Scottish independence referendum remains “off limits”.
Asked whether devolving power more locally in Scotland would make independence more or less likely, the prime minister said: “I don’t want to be the last PM of the UK.
“I just feel we all have to move beyond the constitutional questions.
“In my view, people in Scotland are suffering from the cost of living crisis, like they are in England and everywhere else, and I think our job is to focus on the practicalities, to focus on solutions for people right now.”
He added: “Too much time is wasted on those dramas, it consumes too much energy.”
UK Conservative leader Kemi Badenoch said Burnham should be focusing on creating new opportunities in the energy sector.
She said: “This regional devolution plan is more jobs for the boys. What Andy Burnham should be doing is granting new oil and gas licences in the north sea.”
“Devolution is a process, not a solution.”
