Sterling has been in fine form in recent weeks, with three goals in his last seven appearances in all competitions as Brendan Rodgers' men have found form.
The England international has been in talks with the club over extending his current deal and Liverpool are confident an agreement is close.
Amid some media speculation about possible interest from the likes of Real Madrid, former Liverpool midfielder Barnes believes the 20-year-old should remain at Anfield until at least 2018.
"If I was Raheem Sterling I would stay with Liverpool for the next three years," he told Hinch.as.
"I've seen it with other young players, a lot to do with their agents, a lot to do with the money they have been offered, that they rush off to big clubs.
"Of course Liverpool is a big club, but the temptation must be to go to Real Madrid or Barcelona or wherever, but the danger is that you can be lost to the game, and I can give you so many examples, like Jack Rodwell who went too early to Manchester City and Scott Sinclair who also went to Manchester City.
"With all due respect to clubs like that, they might turn out to be worse for them, and they end up going back and then not getting a move again.
"I would advise young players not to rush, but to stay at their clubs until they are 23 or 24.
"I went to Liverpool at the age of 23 by which time I was a 35-cap international players who could handle it.
"Raheem Sterling going to Real Madrid probably won't play every week, probably will play under enormous pressure to perform as a £50 million superstar, whereas at Liverpool the fans will accept that he doesn't play well all the time.
"I would urge him and players like [Everton's] Ross Barkley to stay where they are, and move clubs in three or four years time."
