With it looking more and more likely that Brendan Rodgers will be able to lure Joe Adam from Swansea, the former Blackpool midfielder will be surplus to requirements and could be used to land Dempsey.
"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."
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