Sterling's future on Merseyside has come into question following reports that he turned down the offer of a new contract worth £70,000 a week.
The 20-year-old has subsequently been linked with a move away, with Premier League champions Manchester City reportedly ready to swoop.
However, Gerrard has urged the England international to stay put and continue his development at Liverpool.
"He can progress here and become a top, top player so I hope the people around him give him the right advice - he should stay," said the Liverpool captain.
"He's great to watch and great to play with. When you look up he's always giving you an option, and that's what I've thrived on throughout my career at Liverpool with the likes of Fernando Torres and Michael Owen.
"Raheem's got the potential to be top drawer, for sure."
Gerrard also warned that Liverpool face a tough afternoon against Arsenal on Sunday unless they up their league performances.
Brendan Rodgers' men responded to last weekend's disappointing 3-0 defeat to rivals Manchester United by beating Bournemouth 3-1 to reach the League Cup semi-finals in midweek.
But Gerrard is well are that the team have to improve in the league.
"Everyone knows if we perform the way we have done of late against Arsenal we'll get beaten," he added.
"It's time to roll your sleeves up and fight for the club and try to put it right as soon as possible and that's what we're trying to do."
