Kilgallon is out of contract this summer and as yet no new deal has been agreed at the Stadium of Light.
The news has alerted Kilgallon's suitors to his possible availability on a free transfer at the end of the season.
The 29-year-old started Paolo Di Canio's first game in charge against Chelsea, but has not played in the last two matches against Newcastle and Everton.
Kilgallon started his career at Leeds before joining Sheffield United in 2009 and, after a hugely impressive one-year spell at Bramall Lane, he was snapped up by Sunderland in in January 2010
The left-sided central defender has a wealth of Premier League experience and clubs are actively monitoring his contract situation.
The likes of Leeds, Crystal Palace, Brighton and Reading are all thought to be tracking Kilgallon as they look to bolster their defensive options next season.