The Italian club, currently mired in the bottom three of the table, are looking for an experienced shot-stopper to add to their squad in January.
And Celtic manager Brendan Rodgers is understood to be willing to allow the 31-year-old keeper to leave either on loan or for a nominal fee.
Bailly joined the Hoops from Oud Heverlee Leuven in July 2015 for an undisclosed fee, but has made only three senior appearances for the club to date.
The Belgium international has not made a Premiership matchday squad this season as Rodgers prefers Dorus de Vries as his back-up to Craig Gordon.
Celtic last week