The 26-year old defensive midfielder has been on song this season for the Italian club with 33 appearances with the addition of 3 goals and 3 assists in Serie A.
If the move were to ever come to fruition, it would mean that he could link up with fellow Slovakian compatriot Martin Skrtel.
"It's good news," Kucka told Dennik Sport. "I have read it on the internet.
"I have not called my compatriot Martin Skrtel and have no plans to do so. I prefer to keep my feet on the ground.
"I am a Genoa player, so I have to think that I'll play in Genoa the next season.
"But I can imagine what it would mean to wear the Liverpool shirt."