The midfielder has been tipped as a possible departure from Marassi this summer, with a number of clubs said to be interested.
However, in considering links with Premier League side Liverpool, the 26-year-old Slovakian has suggested otherwise.
“I’m going to Liverpool? That is good news, I read it on the internet,” joked Kucka to Danish outlet Dennik Sport this week.
“I have not spoken to [fellow Slovak and Liverpool player] Skrtel, and I have no intention of doing so, I prefer to keep my feet on the ground.
“I’m a player of Genoa, so I think that this is where I will play next season, but I can imagine what it means to wear the shirt of Liverpool.”
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