Gerrard, who is now in charge of Rangers, spent 18 months turning out for LA Galaxy, and the 38-year-old has encouraged Rooney to move to North America at this stage of his career.
"I hope he does, I hope he makes it. I enjoyed my time at the MLS and enjoyed the life experience," PA quotes Gerrard as saying.
"I think where Wayne is now in his career I think it would be great for him and his family to go and settle in an incredible state and see a lot of America.
"It is certainly a life experience I'll never forget and I hope he goes and has the same. The league is a good league, the players are fit and mobile and it is competitive and I enjoyed it at that stage of my career."
Rooney scored 10 Premier League goals for Everton during the 2017-18 campaign after sealing a return to Goodison Park.