Rosicky, 33, insists he would love to finish his career at Arsenal, but revealed he will consider his potential options in the next few weeks.
"I would like to carry on but there are a few question marks," he said.
"I would say within a few weeks we will know more.
"If the day comes and I leave Arsenal, then I will be surely considering a move to play on a different continent.
"If it was possible, I would love to end my career at Arsenal, which is something I have said many times before.
"If I should leave, however, then I would be tempted to play in the USA. Football has been on the rise there and I'm interested in trying a different style of life.
"By that, I'm not ruling out a return to Sparta Prague, though."