The Ghana international has long been linked with a move away from Portsmouth, following their relegation to the Championship.
Genoa has also been linked with Sporting Lisbon ace Miguel Veloso.
“Boateng? For me he is the first name on the list,” said Genoa president Gian Piero Gasperini.
“Miguel Veloso? We’ll see, there’s no hurry to sign midfielders. I’ve seen a lot of names mentioned in that role and it is not easy to identify targets.
“The important thing is that the players we get meet our requirements. It may be a day, or a month, it is not a problem.
“The arrivals of (Luca) Toni and Eduardo cover very important positions for us and they are two players who we will look to this season.”
