The LA Galaxy star believes Suarez has burned his bridges with the Kop.
Keane said: "Luis Suarez has been fantastic but he will probably leave the club.
"If you come out with the statements that he has been doing, then I think it's going to be hard for him to stay.
"Whatever the reason is behind him wanting to leave, he's at a massive club, so where would he go from there? I'm really not sure.
"The Champions League is important to a player but if you're playing for a massive club like Liverpool, eventually they're going to be back in the Champions League and they need players like Suarez to help them achieve that."