Suarez has made an impressive start to life at Anfield since signing in January.
Gerrard told the club’s website: “I don’t see why not. He’s still young enough and I’m sure he’s going to get even better than he is now, which is a scary thought. He’s got the appetite for the game to learn and get better.
“Hopefully he will go on here for a long time because he’s certainly got a massive part to play at this club in the future – the history is there to be written.”
