The 35-year-old will be out of contract in the summer and has admitted that he is keen on a move back to Germany, with Bayer Leverkusen his preferred destination.
"I have a contract with Lazio until June and they proposed an extension, but I've received other offers," he told Lancenet.
"I had a few proposals from the MLS and that would be interesting, seeing as Gerd Muller also went to America.
"I'd also like to play another couple of years with Bayer Leverkusen, who were always very kind to me. In any case, I have no intention of retiring, as I want to play for a while yet."
Klose is Germany's joint all-time top scorer alongside Muller with 68 goals.