Nzonzi, 23, joined from French club Amiens in 2009 and signed a five-year contract in August 2010.
"He's asked for a transfer, hence why he never went to [the training camp in] Austria," Kean told BBC Radio Lancashire. "He doesn't want to play for the club any longer."
Kean added: "I had two meetings with his father and he wants to play elsewhere. We'll be listening to offers, but as it stands he remains under contract and we haven't had any offers at all."
Yakubu has already left to move to China and fellow striker Junior Hoilett is expected to follow him out of Ewood Park, but Nuno Gomes, Danny Murphy and Leon Best have all joined Rovers this summer.
Kean added: "It will be natural that we might lose one or two, but it won't be six or seven that we're going to be losing. We're not actively trying to move anybody on."