The Republic of Ireland striker made just one Premier League start last season and was one of those expected to leave this summer as Keane revamped his squad.
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Have your say in our football survey and you could win £100But Connolly has had surgery which will keep him out for four months – almost certainly ruling him out until after the August transfer window closes.
And that makes it highly unlikely that any new club would risk signing him in the summer.
Keane confirmed to the Echo: "Dave had a hip operation the other day and so he'll be out for three to four months. It's a blow for him but at least he will be fit early in the new season."
If Connolly is unable to move in the summer, he would have to wait until the transfer window reopens in January before he can move on.
In the short-term he could go out on loan to a Championship side once he has fully recovered but that was not something which appealed to him last season.
The only other alternative is for Sunderland to pay up the remaining year on his contract and release him, which would allow Connolly to join another club outside the transfer window.
Keane is considering paying up several players this summer, but whether Connolly is one of them remains to be seen.
And the downside is that they would then receive nothing for a player who cost £1.9m when he joined from Wigan back in August, 2006.
Connolly was the club's top scorer with 13 goals when Sunderland won promotion from the Championship 12 months ago.
But after making a handful of appearances, and just one start, at the beginning of last season he dropped out of contention. His only Premiership start was against Birmingham City last August.
A couple of Championship clubs expressed an interest in taking him on
loan last season but he opted to remain on Wearside.
In total, he has made 42 appearances and scored 13 goals for the Black Cats in all competitions.
It is not unheard of for clubs to buy players making their way back from injury – Sunderland bought Andy Reid from Charlton while he was still recovering from knee damage.
But with Connolly having been out of first team action for almost a year, the situation is different.
The full article contains 430 words and appears in Sunderland Echo newspaper.