Najar is said to be have been invited for trials at Arsenal later this year.
But Payne told the Washington Post: "They can talk to him if they would like to get sued. But I don't think it will come to that because Ivan Gazidis [the former MLS deputy commissioner who is now Arsenal's chief executive] is a gentleman.
"We have no intention to have Andy Najar come to Arsenal for a trial. He's under contract and if anybody tries to talk to him, we are prepared to file a lawsuit. This is America. It's American contract law that applies here. Local law prevails. We have not been contacted. I am quite confident that if Arsenal wanted to talk to us about Andy Najar, Ivan would call me. This kid is very, very special."