The French World Cup winner warned in a magazine interview that he did not want to be the "club cretin" where wages were concerned.
The 31-year-old earns about pounds 1m a season with Chelsea after arriving in west London last season from Strasbourg for pounds 2.5m. But the FSA's chairman, Alison Pilling, insists that the extra cash to supplement Leboeuf's salary should come from chairman Ken Bates' pocket and not via an increase in admission prices.
"Most fans believe that Premiership players are paid enough and most would consider they are paying quite enough - and if Franck Leboeuf thinks he is worth more he needs to think about where that money is coming from," Pilling said.
"If he thinks Ken Bates should be putting more money in the club, then most fans would say `fine'. But if it is the fans who should put more into the club, that's a different question. If Franck Leboeuf or any other Premier League player thinks they should be paid more, then they need to give some serious thought to where the money is coming from. If it's out of the profits made by the club, then that's one side. But if he thinks fans should pay more on the gate or through pay-per-view television, that's a very different story.
"At some point, fans will need to sit down seriously with bodies like the Professional Footballers' Association and make sure that both fans and players get what they deserve out of the game."
The former Chelsea defender Paul Elliott has backed Leboeuf in his demand for higher wages from the Stamford Bridge club. He thinks that if the club are to remain among the country's elite they must secure Leboeuf's services for the future.
"You have to say Leboeuf is a top quality defender who has given super service to Chelsea," Elliott said. "Ken Bates is a very decent and reasonable man. If he feels Leboeuf has a justifiable case I'm sure he will put his hands in his pockets. I have no doubt about that.
"Leboeuf is a proven international and is excellent for Chelsea. I am sure the club will want to retain his services and I am sure at some stage in the future it will be best for both club and player to sit down and see if there is a possibility of extending his deal.
"He is a valuable asset to the club, and I am sure that has been more than recognised by Ken Bates."
Leboeuf said in the France Football interview that he hoped to "quadruple" his starting salary when the club enter negotiations over his future.
"Ken Bates likes to say I was the deal of his life," Leboeuf said. "That pleases me, and I'm very happy at Chelsea. But I don't want to be the club cretin.
"I signed a very good contract when I came here. I've doubled it since and I hope to quadruple it soon. If the bosses don't make an effort, I may think about leaving. We'll see at the end of the season."
Roma gave Zdenek Zeman a one-year contract extension Wednesday, keeping the Czech coach on board even though the Italian Serie A club is mired in a serious slump.
The club's spokesman, Dario Brugnoli, confirmed the deal ties Zeman to Roma through until the end of next season, but would not reveal financial terms.
While often providing eye-grabbing play in the attack, as Zeman's teams generally do, Roma, who have won seven and lost six of their 20 matches this season, have faltered of late. They have won just one of their last eight games to slide into a equal seventh place in the 18-team First Division.
Zeman led Roma to a third-place finish last season, his first with the team. He had previously coached Lazio, Roma's city rivals, and Foggia.
The downturn has led to calls, among fans and in the media, for Zeman's dismissal. Such cries reached a peak after Roma's 3-1 defeat on Sunday against Venezia, who are fighting against relegation.
Roma have also drawn with the bottom club, Empoli, and lost to 17th-placed Salernitana in recent weeks.Reuse content