The dramatic development comes after the FIA felt it needed to act on complaints from F1 team principals regarding the activities of the couple.
Toto Wolff is the team principal of Mercedes, while Susie is managing director of the F1 Academy, which is run by F1's commercial rights holders.
It is understood there have been concerns that the pair are privy to information that would not normally be available in regular channels, which could therefore be viewed as a conflict of interest.
The suggestion is that Toto Wolff has access to confidential knowledge about the activities of FOM, which rival team bosses do not have, while Susie is well briefed on team principal discussions which can be of use to FOM.
This has prompted worries that supposedly secret conversations at team principal level could be being passed on to F1's senior management.
A report in BusinessF1 magazine suggested that a comment Wolff made in a recent team principal meeting, based on information that could only have come from FOM, acted as the trigger point for other bosses to complain.
While rival teams have not voiced concerns about the situation in public, it is understood that FIA president Mohammed Ben Sulayem has been lobbied about there being a potential conflict of interest.
In response to that, Ben Sulayem has asked the FIA Compliance Department to investigate.
A statement from the FIA on Tuesday, which did not mention any names, said: "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 into the matter."
Susie Wolff was appointed managing director of the F1 Academy in March this year having most recently served as team principal and latterly CEO for the Venturi Formula E squad between 2018 and 2022.
Founder of the Dare To Be Different initiative, a programme conceived to boost female participation in motorsport, the Scot has since been a keynote speaker at major conferences such as the 2023 Pendulum Summit in Dublin.
In her capacity as managing director of F1 Academy, Wolff reports directly to F1 CEO Stefano Domenicali.
