Prime Minister Andy Burnham had one formal meeting with Manchester City chairman Khaldoon Al Mubarak while mayor of Greater Manchester, according to the Greater Manchester Combined Authority.
A GMCA statement said the meeting took place in October 2021 at the UK Government's Global Investment Summit, arranged by the Department for International Trade.
He also met Al Mubarak informally in the stands at a City home fixture in September 2019, when attending Vincent Kompany's testimonial as a guest of the club.
Burnham said on Sunday he would release details of his meetings with senior figures at Manchester City.
It follows criticism of his comments in the wake of the club being found guilty of all charges related to breaches of the Premier League's financial rules.
A GMCA spokesperson said Burnham had been a guest at City home matches on a "small number of occasions" and that the hospitality had been "declared in the usual way".
The GMCA also said representatives of Greater Manchester sporting clubs would "routinely join business delegations" on international visits during Burnham's time as mayor.
It noted this included Manchester United representatives travelling to Austin and Dublin, Lancashire County Cricket Club joining a delegation to India, and City staff supporting visits to China and Japan.
Shadow sports minister Louie French said that Burnham "cannot hide behind the GMCA" and "must take responsibility for this himself" and urged him to "come clean about his relationship with City Football Group".
"This is far from the full transparency that football fans deserve," French said.
"We have been given precious little information about these meetings, what was discussed and what may have been agreed. If Burnham has nothing to hide, why is he being so tight-lipped?
"His bizarre intervention in defence of Man City's owners has raised serious concerns among fans."
An independent commission found City had broken rules over a nine-year period between 2009 and 2018 by creating "sham" contracts with commercial partners to secretly funnel more than £830m into their football operations.
Burnham's previous role as mayor of Greater Manchester has led to questions about his relationship with City's Abu Dhabi ownership, with Conservative leader Kemi Badenoch demanding No 10 release all details of meetings between the prime minister and senior figures at the club.
"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 told the Rest is Politics podcast., external
"I will quite clearly put out there everything that I have done working with them in my previous role as Mayor of Greater Manchester.
"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."
The prime minister initially told the BBC he would be "really concerned" if Manchester City's owners decide to sell up following the guilty verdict before later denying his reaction had "downplayed the seriousness of the findings".
However, some Premier League clubs were so "astonished" by Burnham's stance that sources told BBC Sport they were "concerned" about political interference in the appeal process.
Sanctions are yet to be announced and City have lodged an appeal against the verdict.
