The Uruguayan scored his fourth Premier League goal in 11 appearances for his new club in the 5-2 hammering of Fulham at Craven Cottage last night and Carragher feels that if he produces more performances like that then he could very well become an Anfield legend.
“If he keeps playing like that, I think he'll be a bigger legend than I'll ever be," the 33-year old told the club’s official website.
"He looks a really top player, he plays for the team. It shows he's adaptable and versatile, he can do different jobs for the team.
"We've been flying since Christmas and that's credit to everyone involved.
"The manager's come in and made a big difference. Whatever he's done has worked.
"Players coming in have made a huge difference as well, Suarez is superb.
"I hope I'm not getting too carried away here but I think the performances that he's showed have proved he's going to be a real player for Liverpool, not just between now and the end of season but for years to come."