Di Canio has been out of work since he was sacked by Sunderland last September.
But his UK representative Phil Spencer says the 45-year-old would relish the chance to become Hoops new manager.
He is quoted in a number of newspapers saying: “Paolo would be keen to speak to Celtic.
“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 joined Celtic from AC Milan in 1996 and went on to win the Scottish Professional Footballers’ Associations’ player of the year award in his first season.
He quit the club after just one season following a pay dispute with then-owner Fergus McCann before moving to Sheffield Wednesday.
His spell in charge at the Stadium of Light was dogged by controversy and he was axed just six weeks into the season after failing to win any of Sunderland’s first five fixtures.
• Watch Owen Coyle’s take on the vacant Celtic manager’s role in this week’s BT Sport video