Kavanagh had a successful month's spell at Hillsborough in October and became a crowd favourite in the process - but went back to Wearside after his spell and has remained on the fringes of the first team.
But there could be other teams in for the Republic of Ireland international too although he has in the past admitted that he would favour a move back to S6 after his successful loan spell here.
Keane told the Sunderland Echo: "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."
"There has been more interest in Kav and I will probably sit down with him next week to talk it through, 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."