Manchester City appealed the independent commission's ruling earlier this month as the club seeks to overturn the verdict and avoid potentially severe sanctions.
The Premier League said City had used "sham" commercial contracts as part of schemes to inflate revenue and understate costs by more than £900 million.
City have denied wrongdoing throughout the case and said the commission's opinion contains "clear material errors".
The UK's Liberal Democrats earlier this month urged Burnham to disclose any meetings he had held with Manchester City's owners, Abu Dhabi representatives or related entities. Conservative leader Kemi Badenoch has also called on the British government to release details of meetings between Burnham and senior City figures.
"I've been asked by the leader of the opposition to publish details of my meetings, which I'm happy to do and I'm going to," Burnham said in "The Rest is Politics" podcast, due to be released on Monday.
"I will quite clearly put out there everything that I have done working with them in my previous role as Mayor of Greater Manchester."
Burnham, who served as the mayor from May 2017 to June 2026, said his contacts with the club were not recent.
"None of it is recent, actually, in terms of the meetings I had. I only had one significant meeting, actually, and that was in 2021," he said.
Burnham expressed concern in September that City's owners could sell the club after the guilty verdict, saying they had been "a huge partner in the building of modern Manchester" and "in turning the club into a global force".