The FIA is reportedly unhappy with some of the nose solutions that are currently collecting test laps at Jerez.
Germany's Sport Bild reported on Thursday that a major row is brewing in southern Spain, after top teams Mercedes, Ferrari and Red Bull unveiled cars with mainly conventional low noses for the new season.
Those with the more conventional noses argue that, while the thin noses may comply with the letter of the regulations, they pose a spear-like danger to rival cars in collisions.
Sport Bild said the top three teams want the FIA to re-write the rules to disallow the thin noses on safety grounds.
But the publication said it knows that FIA president Jean Todt is preparing to take the small teams' side.
Germany's Auto Motor und Sport, on the other hand, said the governing body has launched an investigation, aiming to conclude whether some teams have "gone too far" with their 2014 noses.
And the report said even the low-nosed Red Bull and Mercedes teams are being put under the microscope, since the very tips of the noses are almost paper-thin, with the actual crash structure located much further back -- and higher, contrary to the intention of the new rules.
"This fills the letter but not the spirit of the regulations," an FIA source was quoted as saying.