The Uruguay international informed the Reds of his desire to leave Anfield this summer, with Goal revealing Arsenal are preparing a £35 million bid.
However, Rodgers does not want to sell the 26-year-old and is determined to keep him at Anfield ahead of the upcoming Premier League campaign.
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"I spoke to Luis, of course over the last few months, there has been a lot of speculation over his situation. The fact remains the same; we value the player, he had a terrific season for us last year and showed us his quality."
Suarez received a 10-match domestic ban for biting Chelsea's Branislav Ivanovic towards the end of last season, while the previous campaign he received an eight-game suspension for racial abuse.
But Rodgers has insisted that despite his various controversies, Suarez is a top player and is committed to Liverpool.
"That’s something we’ve stressed, what he did was wrong at the end of last season," he added. "That’s the bottom line you can’t do that on the football pitch, but we’ve moved on from that.
"He’s a real competitor, he’s a winner, he wants Liverpool to do well, he wants to be working at the real high level."