But with West Ham struggling in the league, Sullivan has made the offer to a "special" player to try to avoid the "horrendous" prospect of relegation.
Sullivan would not name the player but Real Madrid's Ruud van Nistelrooy has been linked with the club.
"We've offered £100,000-a-week to a player today and we are still not sure we are going to get him," Sullivan told BBC Radio 5 live. "That was a very special player.
"He's got the choice of almost every club in Europe. He has played at the highest level.
"He's down to three clubs and West Ham are the only English club still in the hunt for him.
"We can carry one exceptional player, who would make a difference on that wage, but generally we have to bring the wages down and in the summer we would hope to sign younger players on a fraction of those wages.
"We're have a crisis and you have to have a different strategy to what our long-term strategy will be."
More to follow.
Source: BBC Sport
Source: BBC Sport