Rodgers recently spoke to the Mirror about the American star:
"Clint is a player we've enquired about, it is as simple as that," said Rodgers. "Ian Ayre, our managing director, has spoken with the club to see what the position is. That is where we're at. He's a very talented player, but we don't like to talk about other clubs' players."
Dempsey could be one of the few veteran stars that Liverpool may be able to sign in this summer's transfer window.
Will Dempsey make a move to Anfield this summer?
Even though Steven Gerrard was healthy for a large part of the 2011-12 season, his age and injury history are concerns moving forward. Dempsey could be the star center midielder that Liverpool has lacked when Gerrard isn't available. Together, Dempsey and Gerrard would be a fantastic tandem in the middle of the pitch.
At 29 years old, Dempsey will not be a part of the long-term plan at Anfield, but since the club needs to start winning at a consistent rate next season, he would certainly upgrade the current squad.
If Dempsey wants to play in the Champions League, then the Reds aren't the team for him. However, it's unlikely that any team in England that has qualified for next year's Champions League would be able to offer Dempsey a spot in their starting XI.
The best destination for Dempsey is Liverpool because he can shine with a major Premier League club and continue to develop as a top player in England.