The 33-year-old has not played a Premier League match for the Black Cats this season and his opportunities are unlikely to increase any time soon, with Dean Whitehead and Dwight Yorke preparing to return from injury.
"There has been more interest in Kav and I will probably sit down with him next week to talk it through," Keane told the Sunderland Echo. "I also spoke to him last week about the situation.
"It's a difficult one because as much as I want to keep him I know he wants to play football, and Kav is not the only one in that situation here. As much as I have to look after the club, I have to be fair to the players too.
"Kav enjoyed his games at Sheffield Wednesday but there have been several other clubs in touch about him since. With his experience, I don't know if a loan would be a big benefit for him - it was fine when he was coming back from injury but he doesn't need to go out and prove himself now."