His current contract expires in June 2014 and Klose repeatedly stated he wanted a return to Germany, but the 35-year-old could be reconsidering his options.
“It is a fact that I have received two excellent offers from the USA for Major League Soccer clubs,” he told German newspaper 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.”
Last week Klose scored his 68th goal for Germany, matching the record set by Gerd Muller.
“I want to win the World Cup with Germany in Brazil, that is my priority. We will give our all, though naturally there are other great football nations who have this objective.”