The veteran defender has lined up alongside the captain for over a decade for the
Reds and thinks that the midfielder is the finest player he has ever worked with.
However, Carragher feels that Suarez is not too far behind the England international, despite only playing for the club for just over two years.
"I've played with a lot of top players here and I've always said Stevie is the best player I've ever played with but Luis is on his shoulder," Carragher told the Liverpool Echo.
"He is close and we are all desperate for him to win Player of the Year and he deserves it. Every side has a couple of players who you hope can turn things for you and [Suarez] does it on a weekly basis."
Brendan Rodgers's side beat Aston Villa 2-1 in the Premier League yesterday, with the winning goal coming from a Gerrard penalty that Suarez had won in the second half.