The Reds have been heavily linked with the American international, whose contract at Craven Cottage expires at the end of next season.
Fulham has said the player is not for sale and that it hopes to tie the 29-year-old to a new deal.
Rodgers has, however, told the official Liverpool website, Liverpoolfc.com, it was interested in bringing the player to Anfield.
"Clint is a player we've enquired about, it is as simple as that," said Rodgers.
"He's a very talented player but we don't like to talk about other clubs' players."
Rodgers was, however, willing to discuss the future of striker
"There has been a lot written and spoken about him but first and foremost Andy is a Liverpool player," Rodgers said.
"To consider a loan period for someone the club spent £35 million ($52.85 million) on isn't something we're looking to do at this moment in time.
"Andy will be the same as every other player - if there's ever an offer that comes in we'd look at it as a club and see if it's going to be worthwhile for the club and the team as a whole.
"The club invested £35 million in him. People talk about whether he can fit into my style or not, but if you're a club and you spend £35 million on a player you'd like to think he can fit into whatever style the team plays.
"He's a good player. He'll join the rest of the group next week and we'll take it from there."
Zdrila's stunning rise from amateur promo enthusiast to podcast host is complete as he leads out the final UEFA podcast of the season. Joining the voice of promotion hyperbole is the dashing Mexican Maestro and part-time Harlem Shake instructor, Roberto Arocha, FFA podcast queen Lucy Zelic and Vitor Sobral, LIVE, from London.