The Scottish champions are currently looking for a new boss following the resignation of Neil Lennon last week.
Di Canio has been out of work since being sacked by Sunderland in September.
The 45-year-old is now interested in returning to Parkhead after spending one year at the club as a player in 1996.
"Paolo would be keen to speak to Celtic," Di Canio's representative Phil Spencer is quoted as saying by Sky Sports News. "He played for the club and he certainly has a good relationship with the fans.
"There has been no contact between Paolo and the club, but if there was, it's something he would consider."
Di Canio's managerial career began with Swindon Town in 2011 before a short-lived spell at the Stadium of Light with Sunderland.