Lampard called time on his illustrious Chelsea career to join MLS expansion franchise New York City on a two-year deal ahead of their inaugural season in 2015.
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.”