The 26-year-old Frenchman has played over 100 games for Toulouse since 2016.
Celtic manager Neil Lennon indicates that a deal is close and the player is seen as a replacement for Dedric Boyata, who moved to Hertha Berlin.
"He's a player we've identified for a long time, even before my time here," Lennon told Sky Sports News.
"Hopefully we can get that one over the line soon."
The Bhoys could look to recoup some of the fee paid for Jullien by complete Kieran Tierney's exit from the club.
The Scotland international has been the subject of a failed bid from Arsenal.