Maloney, his brother and fellow promoter Eugene and trainer Jim McDonnell have been asked to appear in front of a disciplinary panel of the British Boxing Board of Control (BBBC).
The board's Southern Area Council has called the meeting in London to discuss allegations that the trio may have breached the terms of their trainers' licences.
The Maloneys trained comedian Ricky Gervais for the contest, while McDonnell coached businessman Grant Bovey, the husband of television presenter Anthea Turner.
"All the licence-holders connected with the Bovey-Gervais fight have been called by our Southern Area Council to appear before them on 5 February," said Simon Block, the BBBC's general secretary.
"They will be called in connection with an alleged breach of regulations."
Possible penalties that could be imposed range from a simple caution to a more severe reprimand, fines, suspension, the withdrawal of licences in the most serious cases or a combination of punishments.
The BBBC were severely critical of the contests, which began when television presenter Les Dennis and comedian Bob Mortimer got into the ring to raise money for the Sport Relief charity appeal last year.
Political journalist John Pienaar and the former lead singer of Spandau Ballet, Tony Hadley, have been signed up for the next contest and are currently in training.
But boxing's ruling body maintains that the bouts could encourage unlicensed boxing and may be dangerous.
Although not illegal, they have called for the bouts to be stopped and say the BBC's refusal to do so displays "naivety and arrogance".
The BBC has defended the programmes, insisting that safety of the participants was always paramount.
Frank Maloney, who managed world heavyweight champion Lennox Lewis, told the Sunday Telegraph newspaper he had done nothing wrong but had to abide by the board's rules.
His brother, Eugene, who currently manages top prospect David Haye, dismissed the board's position as "petty" and claimed the programmes helped make boxing more popular.