The 33-year-old's contract at the Emirates Stadium expires at the end of this season, but the Czech Republic international is eyeing an extended deal.
The former Borussia Dortmund man has not ruled out ending his career at Arsenal, but expressed a desire to experience football on a different continent, earmarking the United States as his favoured destination.
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"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.
"It's hard to leave a top club like Arsenal. It's a club where I have had everything I have ever been searching for in the football side of things.
"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."
Rosicky has made 94 appearances for Czech Republic and hopes to continue his international career in order to play at the 2016 European Championships.
"I have always liked to play for my country and if you have something to offer, it's not easy to give it up," he added.
"I wouldn't like to give up on either [Arsenal or the national team]. I would like to try for the Euro 2016."