Budget caps and struggling engines will be on the agenda at the next meeting of the F1 Commission.
Auto Motor und Sport claims that "comparative measurements" have shown that Renault, owner and engine supplier to the Alpine team, is "at least" 30 horsepower behind Honda, Mercedes and Ferrari.
Renault would like some leeway in the engine performance freeze to catch up.
Christian Horner, whose Red Bull team struggled for years with underpowered Renault engines, thinks Formula 1 should be receptive to the idea.
"If there's a clear deficit under homologation, it's something we should be sensible about," he said at the Hungaroring.
"Otherwise they're locked in for two more years."
Alpine boss Otmar Szafnauer welcomed Horner's support but says there is already an agreement that if a manufacturer falls 1 percent behind in real terms, "good faith discussions" about the freeze will take place.
Those talks will begin at the next F1 Commission meeting, where the budget cap is also certain to be on the agenda.
L'Equipe claims that Red Bull and Mercedes are at risk of having breached the cap last year, although Aston Martin could have committed an even more serious spending infraction.
Also under scrutiny is Dr Helmut Marko's salary at Red Bull, which is reportedly not included in the team's budget cap exceptions for the three most highly paid staff.
The FIA is doing what it can to keep the speculation in check for now.
"We would like to reiterate that the process leading up to the certification of teams is ongoing," a spokesperson said. "None of the teams have been informed of their certification status."
F1's governing body added that the process should be completed "in the coming weeks", adding that speculation about violations is "completely groundless".
