Carragher believes he's made enough of an impact to say he's had a great start to his Liverpool career.
"For me, to say you've started well you have to have performed well over the first 10, 20 or 30 games for your new club," Carragher told LFC magazine. "One game - good or bad - doesn't mean anything.
"Luis has already shown how good he is by playing well in lots of games. I think he's already done enough to prove that he's a top player. Hopefully he'll be here for a very long, long time."
Suarez has not only proven himself in the Premier League in recent months, he's also been outstanding for his country in the Copa America.
"I watched the highlights of their games and Luis was brilliant, the player of the tournament," Carra recalls. "I'm just delighted that we've got him because he's one of the best in the world. We should be proud of the fact that he's here at Liverpool."