The Uruguayan hit the headlines after scoring four goals against Norwich City in their 5-1 victory at Anfield last night.
While Barcelona star Messi and his Real Madrid rival are considered the two best players in the world, Gerrard believes that Suarez is not far off.
"Having worked with him every single day, it's probably less of a surprise to me as it is to the supporters," Gerrard told the club's official website. "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."
Reports have emerged this morning claiming that Real Madrid are preparing to launch a £65m bid for the 26-year-old in January.