The Israel international, whose deal with the Blues is set to expire, is angling for a move to the United States after almost signing for New York Red Bulls last year
The Israeli joined the Europa League winners in 2010, but made just one league start for the club before being sent on loan to first Arsenal and then West Ham.
The 33-year-old has not been offered a new deal at Stamford Bridge, and has now set his sights on securing a move to the United States.
“I’m in talks with several European teams. I’m checking out the options, but to tell you the truth, America is one of my favourite options,’’ Benayoun told the New York Post.
“I’m trying do everything I can to come to America and to play in MLS, and hopefully it works out in the next few weeks.
“If I leave England it will be only for something challenge, a new style of life like America.
“I love America. Any interesting, good city that you have a nice lifestyle I could give my wife and family. It is more important for me to give them a good lifestyle, schools, everything and then hopefully to enjoy football.
“Of course New York would be great. But Chicago, Los Angeles — America has a lot of options.’’
Benayoun's agent, Ronen Katzav, admits they are weighing up a number of offers for his services from European clubs, but, having already come close to signing for New York Red Bulls, the MLS remains the Israeli's preference.
“Last season he was very close to signing with Red Bull, and now we are checking our options. Normally they were very interested with us,’’ said Katzav.
“We also have options in Europe, of Spain, Germany, of course England. But we’re trying to change a little bit the mentality of life a little bit from Europe.’’