The prime minister initially told the BBC of his concerns, 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.
Burnham’s previous role as mayor of Greater Manchester has led to questions about his relationship with City’s Abu Dhabi ownership.
Conservative leader Kemi Badenoch demanded all details of meetings between the prime minister and senior figures at the club are released. The government released these details on Monday.
“As far as we, as the regulator, are concerned, we have a very, very clear course of action that is governed by statute and we are going to follow that course of action and no comment by any politician or indeed any individual is going to affect what we do”, said Kogan.
“Process is going to drive what we do. Process will lead us to a conclusion.
“We cannot reach any conclusion at this stage because we don’t know the outcome of any appeal and once we do then we will act accordingly.”
The independent panel will hold a sanctions hearing – which could take months to convene – to decide the punishment.
City can appeal both the guilty verdicts and the sanction, leaving the club and the league in a state of chaos and uncertainty.
City’s punishment could range from a huge fine, being deducted points or being ejected from the Premier League, to being stripped of the eight trophies they won in the affected period.
Asked how crucial it is that it was resolved as soon as possible, Kogan said: “I think it’s very important.”
Kogan added that the case was “raising very serious issues if Manchester City on appeal is found to be guilty of the allegations within those findings”.
“We are waiting like everybody else to see what the independent panel will do… and then we will bring in a view in terms of our own investigation and statutory powers if we need to do so.
“Our powers relate to individual owners, directors and senior executives. They refer to whether people are in a position to run a club in a way that is safe, coherent and done with probity, and we will be examining those things.”
An independent commission held a 42-day hearing in 2024 that led to the verdict announced last month, with City also guilty of all charges except one relating to non-cooperation with the Premier League investigation.
The commission’s report said that “a number of important club witnesses gave false evidence in key respects and that some knowingly gave untrue and dishonest evidence”.
