The United Kingdom's Serious Fraud Office (SFO) is looking into a deal agreed between Formula 1's commercial rights holder and the FIA back in 2013.
MP Damian Collins has written to the body to ask it to investigate whether payments made to the FIA were illegal.
The FIA has confirmed that, as part of the 2013 bilateral Concorde Agreement deals, it received a £3.9 million sum plus a 1% stake in the championship.
At the time of the deal, F1's commercial rights were owned by CVC Capital Partners.
Collins, who chairs the Culture, Media and Sport Committee, has written to the SFO to ask it to look into whether the matter breaches the bribery act.
The SFO confirmed to the BBC on Friday that it was examining the details to see whether there are grounds for it to begin a more-detailed investigation.
"The Serious Fraud Office is reviewing material in its possession in relation to these allegations," it said.
"All matters referred to the SFO are assessed against criteria to establish whether they may fall within its remit to investigate."
However, F1's chiefs and the FIA have insisted that there was no wrongdoing in the commercial deal, which was aimed at guaranteeing stability for the governing body to continue its regulatory role.
A statement from Formula One Group, which now controls F1's commercial rights, said: "The figures quoted, including the equity stake, were negotiated to ensure that the FIA could continue to provide and enforce a long-term regulatory framework, which provides safety and stability for the benefit for all key F1 stakeholders including teams, drivers, other partners and, of course, the F1 commercial rights holder itself".
The FIA added: "The Concorde Implementation Agreement entered into by the commercial rights holder of Formula 1 and the FIA in 2013 introduced a new governance structure for Formula 1 and redefined certain conditions applicable to their relationship, in particular to ensure that the FIA be properly remunerated for its regulatory role.
"Within this agreement, a lump sum payment of $5m (£3.9m) was made to the FIA as part of the global consideration received in connection with the renegotiation of the terms of the agreements between the commercial rights holder and the FIA, and of the Concorde Agreement, at that time.
"Following its approval, the Concorde Implementation Agreement came into force and this sum was paid to the FIA and properly accounted for.
"No individual received any payment out of this sum. Any allegation to the contrary would be defamatory."