The Black Cats boss was playing his cards close to his chest in the after-match conference when quizzed if the former Wales international was going to be on his way to the Stadium of Light when the transfer window opens on Tuesday.
Former Manchester United midfielder Quinton Fortune has also been linked but Keane was giving nothing away.
He said: "There have been plenty of players linked with us. I would say in the last month maybe something like 20, 25. I don't think we will be signing 25 players, let me tell you.
"It would be completely wrong for me to comment on a player under contract at a football club.