Sterling, 20, has been embroiled in protracted negotiations over a new five-year contract but there is no clear indication yet whether he will sign the deal or look to move elsewhere this summer.
Speaking in his final press conference as a Liverpool player ahead of his last competitive game at Anfield, Gerrard says Sterling will not get a better manager to develop him than Brendan Rodgers.
The 34-year-old said: “In my opinion he should sign a new deal, but that’s something I can’t control.
“My advice to Raheem is he needs a manager who believes in him and will help coach him – and there’s no one better than Brendan Rodgers for that.
“Brendan is a fantastic man-manager. The danger is these younger players want it all too soon but they go to another club and become just another number.”
Midfielder Gerrard, who will move to LA Galaxy this summer, is set for an emotional goodbye at the club at which he has spent 17 years and supported since he was a boy.
The former England skipper thanked all the managers he has played under over the years, from Gerard Houllier to Rafa Benitez, but reserved special praise for current boss Rodgers.
“I wish I’d met Brendan in the peak of my playing days because I think we could have won lots of trophies together,” said Gerrard, who has been described by Sky Sports’ Thierry Henry as a “special” Premier League player.
“He’s been great with me, great for the team and great with the young players. If they’re good enough, Brendan has shown he will give them the chance, but first and foremost, they have to be good enough.”
Watch Steven Gerrard’s final home game against Crystal Palace on Saturday Night Football, with coverage starting at 5pm.