The Turkey international is the latest forward-thinking talent to be linked with a January switch to Anfield.
Liverpool have already acquired the services of Daniel Sturridge, and Brendan Rodgers is said to be keen on bringing in Turan to provide ammunition from the flanks.
Atletico are aware of the rumours, but insist there is no substance to them.
Coach Diego Simeone insists no transfer discussions have been held, with there a strong desire on his part to see Turan remain in the Spanish capital.
He said: "First, I have not heard anything and I have seen it a lot. Everyone can comment on whatever you want.
"The important thing is what he shows on the field. Arda is one of the best players. He shows heart in every one of our matches.
"He has a contract with our club and he shows everyone what he has to offer."