Gerrard, who retired from England duty at the end of the World Cup, has been at Liverpool since emerging from the youth team in 1998 - amassing 475 Premier League appearances and 111 goals.
The 34-year-old midfielder - in the United States for Liverpool's pre-season tour - has a year to run on his contract and admitted playing in a league such as the MLS could be on the cards.
"One day that might happen to me, I don't know," Gerrard told reporters.
"I've never really discussed it with anyone or thought about it. Maybe one day I would like the chance to go away from Liverpool for a short time and try something different.
"I think Frank has made a great decision. At his age, 36, he's had a wonderful career and I don't think he has anything to prove in England in any more.
"He's broken records with Chelsea and won everything with them. I think it's a perfect move for him. But I haven't given it much thought. That carrot hasn't been dangled yet."
Gerrard only has a year left on his Anfield contract to run, but has made no secret of his desire to extend his time at Liverpool, and is hoping a new contract could be discussed in the very near future.
"Brendan has mentioned it a couple of times in the media but no talks have happened," said the 34-year-old to the Daily Telegraph.
"I'm sure we will talk in the future, but we will have to wait and see. I hope that I am here for more than one year, of course I do. But it is all about this season for me."