The 33-year-old Israeli midfielder has spent eight years in the Premier League following spells with West Ham, Liverpool, Arsenal and the Blues. However, with his current spell at Stamford Bridge coming to an end at the end of June, Benayoun has ruled out the possibility of staying where he is or joining another Premier League side.
And while the playmaker has options to move to other European clubs, he is desperate to ply his trade in the United States.
Benayoun said in the New York Post: "I finish my contract on 30th June. At the moment I'm in talks with several European teams.
"I'm checking my options but, to tell you the truth, America is one of my favourite options.
"I'm trying to do everything I can to come to America and play in the MLS, and hopefully it works out in the next few weeks."
New York Red Bulls are thought to be vying for Benayoun's signature and the player's agent Ronen Katzav would not rule out a move.
He said: "Last season he was very close to signing with the Red Bulls, and now we are checking our options.
"We also have options in Europe - Spain, Germany and, of course, England a few clubs, top leagues.
"But we're trying to change a little bit the mentality of life a little bit from Europe. You know when you are a football player, one of the things is to test. To test things and maybe to change some things to another country, another mentality, another way of life and another football. This is the way we are looking."