The Serious Fraud Office are currently "reviewing material" relating to a £3.9million payment made by Formula 1's commercial rights holder to the FIA.
MP Damian Collins has raised the potential issue after revealing that he was "very concerned" why such a payment had been made and could be in breach of bribery laws.
"That's why I've written to the Serious Fraud Office (SFO) asking them 'do they feel there was a breach of the Bribery Act and does it warrant investigation?'" said Collins, who is also the chairman of the Culture, Media and Sport Parliamentary select committee.
An SFO spokesperson added to BBC Sport: "The Serious Fraud Office is reviewing material in its possession in relation to these allegations. All matters referred to the SFO are assessed against criteria to establish whether they may fall within its remit to investigate."
The FIA confirmed in a statement that it had received the payment and explained: "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."