Boateng is said to be keen on leaving Fratton Park following Pompey's relegation to the Championship and Serie A could be a possible destination for the player.
But the 23-year-old's representative says Genoa have not been in touch with him over a deal - nor has there been any contact between the two clubs.
Mario Miele told pianetagenoa1893.net: "We are still waiting a call off Genoa, probably this week we have an appointment with the leadership of Rossoblu club.
"Last week we talked with management of Genoa for what concerns the employment of the player.
Reports had circulated that Boateng was not keen on a switch to the Luigi Ferraris outfit, although Genoa were coy on such suggestions.
Sports director Stefano Capozucca told tuttomercatoweb: "If Boateng refused to come to Genoa? These are all rumours, there's nothing official."
He added in La Repubblica: "Lazio (interested in Boateng)? It is a distant hypothesis, but everything can change in football. Never say never, because we don't hurry."