The 36-year-old has spent just over two seasons at the Stadio Olimpico and has gone on to score 32 goals from his 75 outings.
However, the centre-forward admits that he could either continue his career in the MLS or return to his first club Kaiserslautern in 2014.
"I have two offers from the States and I could return to Kaiserslautern where I started my career," he told La Gazzetta dello Sport. "I will make up my mind in the next few months."
Klose has also played for Werder Bremen and Bayern Munich.