Fulham have said the player is not for sale and that they hope to tie the 29-year-old to a new deal.
Rodgers has, however, told the official Liverpool website, Liverpoolfc.com, they were interested in bringing the player to Anfield, saying: "Clint is a player we've enquired about, it is as simple as that. Ian Ayre, our managing director, has spoken with the club to see what the position is. That is where we're at."
He went on: "He's a very talented player but we don't like to talk about other clubs' players."
"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 £35million 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 £35million in him. People talk about whether he can fit into my style or not, but if you're a club and you spend £35million 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."