The pair have been at the forefront of Liverpool's Premier League title charge, which was strengthened by rivals Manchester City and Chelsea both slipping up against Sunderland this week.
A top-four finish was the stated aim this season for the Reds, who have finished no higher than sixth in the past four campaigns, but they have thrived under Rodgers.
Gerrard told the Daily Telegraph: "He's a phenomenal man for his age (41). I think he's going to grow into one of the world's best managers and I hope he is here long after I am gone.
"I hope he is here for many, many years because this club is in great hands. Whatever happens now until the end of the season, it's safe.
"He's a winner, he's hungry for success, he does the right things, he treats players well, he doesn't try and control the football club, or get involved in stuff that has nothing to do with him.
"He just focuses on getting on the training pitch and coaching the team, improving individuals, improving the team and playing football the right way. That's what the supporters want here."
The Merseysiders currently top the standings by two points, ahead of today's clash with Norwich, and are now firm favourites to earn their first league success in 24 years, with captain Gerrard admitting he will need to keep his emotions in check during the run-in.
"They are there - the nerves, the excitement. They are there because we have earned the right to have those kinds of feelings," he added.
"The challenge for me, which just as important as being on the pitch now, is can I control myself and can I get on with my life for the next four weeks."