The Irishman has been linked with a summer exit from the Stadium of Light with a quartet of Premiership sides ready to pounce.
Sunderland claim Aston Villa, Everton, Southampton and Kilbane's former club West Brom have all made enquiries about the 24-year-old.
However, Saints chairman Rupert Lowe has dismissed the comments and also that the club are eyeing Coventry City goalkeeper Magnus Hedman.
A third player linked with a move to St Mary's was Phil Babb with Lowe insisting he was not on Gordon Strachan's shopping list prior to the defender's switch to Sunderland.
"Kilbane is a good player but we have not made any kind of enquiry for him or for either of the other two, so there is no truth in any of those reports," Lowe told the club's official website.
"We are still aiming to strengthen in one or two areas and we have a couple of possibilities we are looking at."
