The Reds captain feels the Uruguay international is capable of going on to become one of the best players in the world if he continues improving.
The Uruguay international continued his emphatic season on Wednesday with a four-goal haul as the Reds saw off Norwich 5-1, meaning he has now scored 13 times in just nine Premier League games.
Gerrard feels such performances from Suarez prove he is edging ever close to becoming one of, if not the greatest in the game.
"You have seen a world-class performance, probably one of the best individual performances I've seen at Anfield - and I've been playing here a long time," the Liverpool captain told the club's official website following the win against the Canaries. "Having worked with him every single day, it's probably less of a surprise to me as it is to the supporters. I've been pushing his corner for a long time that he is up there with the best in the world.
"I think he's getting so close to the main two, Ronaldo and Messi. If he keeps going, I think he can catch them. His fourth goal was average and it was a 30-yard free kick, so I think that sums his performance up."
The thrashing of Norwich was the perfect response to the surprise loss to Hull City on Sunday, and Gerrard hopes Liverpool can replicate the display in games to come.
"That's what the manager [Brendan Rodgers] asked for - a big reaction," Gerrard added. "It was a bad few days after Hull, everyone was down and we weren't proud of the performance. We let ourselves down. There have been a couple of occasions this season that we have done it and come unstuck. One was Southampton at home and one was Hull away. Hopefully there are not too many more. At home against the teams lower down the league we have been ruthless and that's what we showed tonight. We were ruthless from the first minute.
"It was all about the reaction tonight and the three points. We're really pleased but we've got to match that again against West Ham or tonight is pointless. We have been really good at home, for the majority of games we have been superb. There was only Southampton where we haven't turned up. If we keep performing to that level, we can make Anfield a fortress. If you want to be successful in this league, you've got to make your home ground a fortress."