The 30-year-old is said to have told the club he wants more first-team football and, even if the west London outfit don't want to let Cahill leave, he has several days left in the transfer window to try and force a move if he isn't guaranteed any game time.
Liverpool, meanwhile, are short of fit centre-backs, while Cahill is arguably superior to all of their first-choice defenders, anyway.
A move may be unlikely but the betting clearly favours the Reds if the England man is to leave Chelsea.
And how do Liverpool fans feel about the speculation?
Well, their views are emphatic - and not in the usual way when anything Chelsea related is concerned. Indeed, supporters want the 30-year-old at Anfield. Cahill is a very capable defender and the prospect of such a signing certainly excites the Kop.
Here's how Liverpool fans have reacted on Twitter to the Cahill transfer talk...
Gary Cahill would be a decent signing for our defence! Don't believe them rumours though. #LFC— •Bobzi|LFC• (@ByronBobzi) January 27, 2016
Cahill wants out of Chelsea? I'll be honest, don't think he's world class but he'd certainly improve #LFC at the back at the moment.— Michael James Field (@Mikuss) January 27, 2016
Gary Cahill wants to leave Chelsea for first team football, Klopp get on the blower, make a offer and get him in ASAP!! #LFC— Adam Knight (@knighty_316) January 27, 2016