The Daily Mail reported that the Serie A champions are readying an offer for the 25-year-old, who is yet to extend his contract despite holding talks with the Anfield hierarchy.
But, the newly-appointed manager has dismissed any possibility of the Uruguayan wanting to leave, and stressed that Suarez is, instead, looking forward to the start of the new Premier League campaign.
“I’ve had a brilliant chat with Luis,” Rodgers told TalkSPORT on Tuesday morning.
“He’s really looking forward to being here and we are obviously hoping that we can get him on to another new contract. He’s really looking forward to the new season.”
Rodgers has yet to land his first Liverpool signing, after seemingly being beaten by Tottenham to the signature of Gylfi Sigurdsson, but the coach revealed plans to bring fresh faces to Anfield this summer to “make a difference” after the club’s poor league form last season.
“I’m looking forward to bringing in three or four players that can really affect the group,” he confirmed.
“I’ve got a wonderful group of players here at the moment.
“I read every day players that are linked with here and unfortunately, especially for the supporters, it’s a difficult time because you've got agents linking players with Liverpool just purely because it's great for them to be linked with such an institution of a club.
“But the reality is there are very few players who can come and make a difference to Liverpool.”