Toto Wolff and Susie Wolff had been named by Motorsport as those being investigated.
An FIA statement read: “The FIA is aware of media speculation centred on the allegation of information of a confidential nature being passed to an F1 team principal from a member of FOM personnel.
“The FIA Compliance Department is looking in to the matter.”
Formula 1's response was: "We note the public statement made by the FIA this evening that was not shared with us in advance.
"We have complete confidence that the allegations are wrong, and we have robust processes and procedures that ensure the segregation of information and responsibilities in the event of any potential conflict of interest.
"We are confident that no member of our team has made any unauthorised disclosure to a Team Principal and would caution anyone against making imprudent and serious allegations without substance."
Mercedes' statement read: "We note the generic statement from the FIA this evening, which responds to unsubstantiated allegations from a single media outlet, and the off-record briefing which has linked it to the Team Principal of Mercedes-AMG F1.
"The Team has received no communication from the FIA Compliance Department on this topic and it was highly surprising to learn of the investigation through a media statement.
"We wholly reject the allegation in the statement and associated media coverage, which wrongly impinges on the integrity and compliance of our Team Principal.
"As a matter of course, we invite full, prompt, and transparent correspondence from the FIA Compliance Department regarding this investigation and its contents."