HITC Sport understands several clubs are tracking the former Blackburn defender.
Former Sunderland and Leeds defender Kilgallon is currently a free agent after seeing out his contract at Ewood Park earlier this summer.
Kilgallon was not offered a new deal by Blackburn along with several other players because of confusion over who would be the club's manager as Owen Coyle was not appointed before the players who were out of contract were allowed to leave.
Kilgallon is an attractive proposition for his suitors as he boasts a wealth of experience having played the majority of his career in the Premier League and Championship.
The left-sided central defender can also fill in at left-back and his versatility has alerted several sides as they look to bolster their defensive options before the start of the new season.
The 32-year-old, who came through the ranks at Leeds United, has made over 300 first-team appearances in his career to date and captained Blackburn in the 2014/15 season as they reached the FA Cup quarter-finals.