The Germany international's contract with Lazio expires at the end of the season and Klose admits he is keeping his options open.
Klose admits the two offers he has received from America are 'excellent' and that he does not know what his future holds at the moment.
"It is a fact that I have received two excellent offers from the USA for Major League Soccer clubs," Klose told Bild.
"My contract with Lazio goes on for another year and who knows how it will end? I don't want to rule anything out at this moment.
"Do I have a future at Kaiserslautern? They are and always have been a club close to my heart. Mesut Ozil's move to Arsenal proves once again that you can't rule anything out in football.
"One minute you're happy at a club and the next you're somewhere else."