The Germany international's contract with the Serie A outfit expires at the end of the season and though they are keen to keep him on, the 35-year-old could look elsewhere.
Klose, who last week equalled Gerd Muller's record of 68 goals for Germany, has previously expressed his desire to return to his home country but he admitted that the offers from America are "excellent".
"It is a fact that I have received two excellent offers from the USA for Major League Soccer clubs," he 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."
Klose has been with Lazio since 2011, having played for Bayern Munich for four years before that.
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