Arsenal chairman Peter Hill-Wood has revealed Ashley Cole wanted to see his salary tripled in recent discussions with Highbury officials.
And he also raised fears at the rise in "player power" in the wake of the Bosman ruling.
"If you take someone like Ashley Cole, he has another two years to go," Hill-Wood told the Evening Standard.
"He wanted something like three times what we are paying him. We said we can't do that."
Cole, who is believed to be on a salary of £27,000 a week, and his agent Jonathan Barrett have been involved in negotiations with the Gunners.
It is thought the club turned down an inital demand of about £70,000 a week but then put forward a "final offer" of £55,000 to the player, which Cole is reported to have rejected.
The England defender was also recently involved in a two-day hearing into the "tapping up" affair with Chelsea.
Cole is accused of approaching Chelsea and the Blues, manager Jose Mourinho and chief executive Peter Kenyon have been charged with approaching him.
Hill-Wood added: "We have no control over the players now, they control us.
"The Bosman system has meant that the power is really in the hands of the players and their agents now. You can't stop players leaving.
"Talks are still going on with Ashley Cole, as they are with Thierry Henry, Patrick Vieira and Freddie Ljungberg.
"I want to make it clear none of them have been a problem to us, none at all. And they all have two years left.
"Because of that, we have to re-negotiate now. But with Bosman, we haven't got any cards to play if they say they don't want to sign a new contract."
Earlier on Thursday, Wenger said he believed the Cole saga had damaged the club's season, while Chelsea have escaped without any ill-effects.
He told BBC Radio Five Live: "Damage has been done to Arsenal. What happened has influenced our season but it didn't influence Chelsea and we have done nothing wrong."
A two-day inquiry into the meeting between Cole and Chelsea - which allegedly was held at a London hotel in January - ended on Wednesday.
The independent commission will now consider its verdict and announce its decision on 1 June.
Wenger believes that the hearing - and any subsequent punishment - have come too late to have any effect on Chelsea.
When asked what punishment he wanted to see handed out, Wenger said: "It's up to the Premier League to decide that.
"I don't think they will be harshly punished, which should have been done a long time ago. A harsh punishment is first of all a quick punishment."