Manchester City and Paris Saint-Germain have called on UEFA to give clubs more time to balance their books under financial fair play (FFP) regulations.
European football's governing body has penalised clubs that made losses including City and PSG, who were both fined 40 million pounds in the summer for failing the "break even" test.
Now the Premier League and Ligue 1 champions have lobbied for the three-year FFP monitoring period to be extended by up to 10 years.
The clubs made their case at talks on Monday at which the future of FFP was discussed, and Lyon president Jean-Michel Aulas said earlier that he would back PSG's stance.
UEFA wants FFP to prevent clubs from "reckless spending and financial insanity" but some have voiced fears that it will make the existing European elite a closed shop by preventing other clubs from becoming competitive quickly.
RMC reported that PSG president Nasser Al Khelaifi strongly defended the club against heavy criticism from his Bayern Munich counterpart Karl-Heinz Rummenigge.
Earlier, Rummenigge had been quoted by goal.com as saying that an extension to the FFP monitoring period would allow heavily-backed clubs such as PSG to "invest indefinitely -- and we don't think that's fair."
He stressed that he did not "condemn PSG" and added: "I understand them, even. The club was in the darkness for 20 years until a sheikh took them over."
RMC reported a source close to UEFA as saying: "For more than 15 minutes, he defended his club with strength and conviction. He was very convincing. The exchange with Rummenigge was very tense."
Prior to the meeting, UEFA president Michel Platini had said he was open to discussion about potential changes to the FFP rules.
And speaking afterwards, he said: "Today's meeting was very constructive and again showed that the main concerned parties in Europe wish to work together in order to create a healthy financial context for club football.
"We have managed to reduce the total losses of European clubs and stabilised football's finances on the continent. We now have to work together to ensure the clubs can grow and prosper in the future."