Alexei Lalas, Tab Ramos and Jeff Agoos have all said they will refuse to play under Sampson, having voiced strong disapproval of the US team's tactics and selection.
The Americans lost all three of their group games, ending with Thursday's 1-0 defeat by Yugoslavia. Sampson's future as coach will be decided within the next month by the United States Soccer Federation.
Sampson has promised the fines would be "significant" and that he would not pick any of the players concerned if he retains his job.
"I don't think any level of unprofessionalism is acceptable," said Sampson yesterday, particularly stunned by Ramos's comments that the Americans' campaign has been a "mess".
"It's unfortunate he feels so free to voice his opinions about me when I have given him so much respect and credit," the coach said.
Midfielder Predrag Radosavljevic, upset at not being in the starting line-up against the country of his birth, may also be disciplined and Sampson revealed he had considered sending the bearded Lalas home following an outburst after the first group game against Germany.
"His professionalism was top class but his mood once we lost changed dramatically," said Sampson, stressing he had always regarded Lalas as a back-up defender in France.
"In my opinion you earn the right to represent your country."
Sampson himself rejected the suggestion he might resign. "I've worked too hard... I'm not going to let one or two individuals dictate my career."
But he added that if he failed to be reappointed as coach he would be interested in the role of heading the US Federation's new "Project 2010", aimed at improving football standards in the States.
One option could be for Sampson to be moved sideways to front Project 2010, an attempt to develop a structure in the United States to give the national team a realistic chance of winning the World Cup in 12 years' time.
"If they consider it's a matter of poor execution by the players, I think they should retain me," he said. "They have every reason to dismiss me if they think it is a case of poor preparation or tactics."
The players earned $35,000 apiece from the tournament, but the exact size of the fines has yet to be confirmed. "Those concerned will be notified by letter over the next few days," Sampson said.
Sampson should soon know whether the poor showing has cost him his job.
Alan Rothenberg, president of the US Soccer Federation, said a decision would be made "within 30 days" on whether to reappoint Sampson, who took over in April 1995.
Under Sampson, the United States beat Brazil in the Concacaf Gold Cup in February, but have otherwise struggled to score goals on a regular basis.Reuse content