Danish newspaper Politiken claims it has seen documents suggesting Laudrup's agent, Bayram Tutumlu, could have made more than £3m during the Dane's reign.
It claims Swansea accused the two of trying to "benefit from transactions at the expense of the club".
However, chairman Huw Jenkins said he sacked Laudrup for "football reasons".
Laudrup told BBC Wales Sport: "I have never received any payment or commission related to any player transfer in any of the clubs I have coached. Never."
The former Denmark international was appointed in June 2012 and led the Swans to their first major trophy when they won the 2013 League Cup - but he left the club after less than two seasons in charge.
The Swans cut all ties with Tutumlu in June 2013 following concerns he was trying to dictate transfer policy, with the club perturbed by his attempt to sell then-captain Ashley Williams without the board's consent.
A poor run of form left Swansea two points above the Premier League relegation zone and Laudrup was sacked in February 2014 - but he insists his departure had nothing to do with any irregular payments.
"I have read that Swansea stated that they have not found anything that indicates that I have done something wrong or illegal regarding the player transfers in my period as a manager in the club," he said. "I knew that but it is a relief that the club confirms it."
The Politiken article was based on documents it says were obtained in collaboration with Football Leaks.
According to the article, Swansea wrote a letter to the League Managers' Association (LMA) when Laudrup was sacked, claiming there were "a number of transactions and dealings with players about which the club has concerns".
However, speaking to BBC Wales Sport, Jenkins said the club did not suspect the former Barcelona and Real Madrid player of any wrongdoing.
"There were discussions with the LMA but that was done in the context of negotiating a settlement and it should be taken in that light," he added.
"As far as we are concerned that is the end of the matter and we agreed a settlement and we move on."
Tutumlu has represented Laudrup since the 52-year-old played for Barcelona from 1989 to 1994.
According to the Politiken article, the documents show Jenkins signed an agreement which would give Tutumlu 7.5% of the net profit from all player sales when Laudrup extended his contract in March 2013.
Tutumlu has yet to respond to BBC Wales Sport's request for comment, but Jenkins says that particular clause never came into effect.
"On that particular point it was never acted upon and as most people know transfers in and out of the club are controlled and decided by myself, always in conjunction with the manager," he added.
"But ultimately we had the control and from that date to Michael's departure in 2014 that point in particular was never active.
"All I can say as far as I am concerned is we dealt with everything in the right way as we saw it and in good faith."
Former Swansea City manager Michael Laudrup has denied he was sacked because of concerns he and his agent stood to profit from player transfers.