The Association of Tennis Professionals (ATP), the governing body of the men's game, wants up to 30 percent of revenue from the four major tournaments to help fund the tour.
Around 100 players met at the All England Club at the weekend to hear a proposal to stage rival tournaments during the Australian, French and US Opens, and Wimbledon in 2004.
ATP chief executive officer Mark Miles said: "We have players who want to create alternative events to run against the Grand Slams.
"If we ever got to the point where the players became convinced that the Grand Slams are simply not willing to deal, from our perspective, reasonably with the players' concerns, we would be prepared to make other plans.
"Our preference is for patient cooperation and discussion."
And Todd Martin, president of the ATP's player council, admitted Wimbledon officials have yet to be convinced.
"No one wants to miss any events but we will take action. Initially, the Wimbledon reaction was defensive in the true sense of the word. They have told us what they do with the money. We are continuing the dialogue to find a consensus with the Grand Slams individually."
