The Serie A outfit have been leading the hunt for the Portsmouth midfielder for some time, and were believed to be closing in on an agreement.
However, talks with Pompey and Boateng's representatives have come to halt, leaving the Ghana midfielder in limbo.
A deal could yet be resurrected, with either Genoa or their Serie A rivals Lazio, but for now the 23-year-old must be patient.
"I don't think the talks can be considered closed," Boateng's agent, Mario Miele, told lalaziosiamonoi.it.
"We are always in contact with Genoa and it was they who informed us of the interest from Lazio, as we have never spoken to them directly.
"Until a few days ago there was constant dialogue and everything seemed to be coming towards a conclusion, although Portsmouth were still asking for more.
"But since then everything has reached deadlock. I don't think everything is over, because no-one has told me that, so I suppose the interest is still there.
"We will have to wait and see what happens now over the coming days."
Miele is confident something can still be put in place, especially as Boateng has no shortage of admirers.
He added: "The market is slow right now, even if there are a lot of clubs interested in the player.
"A few days ago I heard that Liverpool and Everton were keen, and also Besiktas. Today I have read that Stoke are interested, but I know nothing about that."