The Italian is reportedly on Ronny Deila's radar as he looks to add experience to a youthful Hoops side.
The 32-year old began his career in the Milan youth set-up but failed to make a first-team breakthrough and was sent out on loan twice, before making a permanent switch to Sampdoria in 2003.
Regular playing time again proved difficult and a further four loan spells followed before the full-back made a brief switch to Empoli.
He rejoined Milan in 2008 and enjoyed the most consistent period of his career, featuring regularly for the Rossoneri over a five-year spell.
The summer of 2013 saw Antonini once again exit the San Siro - this time for Genoa – but his productive first season was followed up by a campaign to forget last term.
He managed just three Serie A starts and seven appearances in all, last time around, and could view a move to the Scottish champions as a chance at a fresh start.
Emilio Izaguirre has been a consistent performer but there isn’t a great deal of support beyond the Honduran.
Antonini could provide just that, and Celtic will be hoping that the lure of Champions League football is enough to convince him to swap the Italian coast for the East End of Glasgow.