The new Williams FW35 features a two-part vane behind the exhaust, mounted at the top of the u-shaped channel into which the exhaust pipes exit, while Caterham has a similar one-piece part placed a little lower.
Technical director Mike Coughlan was adamant that the part is legal when asked about it in the wake of the car being unveiled on Tuesday morning.
He believes the fact that the vane is in two parts makes it permissible, whereas he sees the Caterham design as illegal because it is a single piece and fully encloses the Coanda channel.
But the Williams team has confirmed that the FIA approached it on Tuesdy morning to express its view that the design, along with that of Caterham, is illegal.
The FIA insists that an exhaust's primary purpose must not be to affect the aerodynamic performance of the car, a stipulation governed by a combination of the technical regulations and private technical directives issued to the teams.
In order to ensure this is not happening, it deems that the sides of the Coanda channels are not allowed to converge in any way, meaning that they must be vertical or slope outwards.
Exhaust gases are allowed to have an incidental aerodynamic effect, but what Williams and Caterham have attempted is understood to be seen as overstepping the mark.
Despite the FIA's concerns, its current position is only advisory and both teams can continue to run their designs during testing, which is unregulated beyond safety standards.
Should they continue to run them once the season starts, the FIA is able to refer the matter to race stewards for consideration.
When contacted about the situation, a spokesperson told AUTOSPORT: "The team spoke with the FIA this morning (they approached us), which is when they gave us their view.
"The team are now seeking further clarification on this and a decision as to whether this design will be carried forward will be made before the first race."