The Uruguayan striker scored twice in the Reds' 3-0 win against Sunderland on Wednesday and was also twice on target on Sunday when the Merseyside club got the better of Redknapp's QPR by the same margin.
"I was talking with Harry after our game, and he said Luis was a Messi-type character," the Daily Mail quotes Rodgers as saying.
"When I gave him a break at the start of the season, he didn't want it. He didn't want the breather.
"He is a player that has to play two or three times a week to be on top of his game - one game a week is no good to him. He needs to be playing."
Rodgers further praised Suarez for his consistency and work ethic.
"And you see the response you get from him," he said. "His work has never dropped. He is a real team player and trains every day.
"He is never in the treatment room and then he comes out and performs. As the ball moves, he finds the spaces.
"His cleverness finds the space, and he is thriving. It will be fantastic to see him keep developing."
Liverpool are now eighth in the Premier League table with 31 points from 21 matches.