It is believed the deal is worth to up to £8 million, which would make Jullien the second most expensive player in Celtic's history of the deal goes through.
That looks increasingly likely to happen with L'Equipe reporting that Jullien has agreed terms and is ready to put pen to paper on a long-term contract.
The 26-year-old will help offset the loss of Dedryck Boyata and Filip Benkovic this last summer.
He will also become Celtic's first signing of this window unless the club can finally get their move for David Turnbull completed.
The Motherwell player's on-again-off-again move to Neil Lennon's side has gone on for a number of weeks, with latest reports suggesting a knee injury has left the transfer hanging in the balance.