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Speaking ahead of Burnham's visit, First Minister Michelle O'Neill called for a "fair budget settlement that actually works for public services".
"The reality is that we are so underfunded - have been for years," she told reporters on Wednesday.
"If Andy Burnham wants to make a difference, then he can make a difference by actually changing the funding arrangement, because what we have currently does not cut it."
Talks between Treasury officials and the executive have been taking place over the summer.
On Monday, Northern Ireland secretary Sir Chris Bryant said it was "shocking" that a Stormont budget had yet to be agreed.
He said the executive could consider more "self-help" in the form of revenue-raising, but where there are "significant" budgetary pressures he wanted to be able to help.
Before the prime minister meets politicians he will hear from young people about the issues that impact their lives and their aspirations for the future.
This will include the Prime Minister speaking with teenagers and staff involved in mentoring schemes within Belfast's creative music scene - which seeks to elevate local artists and promote the city as a UNESCO City of Music.
"People in Northern Ireland want more breathing space from the cost of living, good, well-paid jobs and opportunities for their children," he said.
"Political point-scoring in the past has made this harder, not easier. We need to be better, so I want to work with the Northern Ireland Executive and the main political parties to try and make a real difference to communities here, and that's the message I'll be taking into my meetings later," he added.
Earlier on Thursday, Burnham travelled to south Wales - his first official visit to the country since he became prime minister.
Before the trip Burnham announced plans to bring together the leaders of Wales, Scotland and Northern Ireland in the autumn for a summit to help boost the UK economy.
