The 28-year-old has been around Ligue One for many years and has earned one international cap for France.
Once linked with Arsenal, Ciani is into the final year of his contract and could be available at a knock-down price.
Newcastle and Wigan have also been credited with an interest, but reports in France today claimed the Parkhead side have opened up talks with the player's agent.
Meantime, Celtic will prepare for their title defence and Champions League qualifiers with three games in Germany next month.
Neil Lennon's side will play Bundesliga club FC Augsburg on July 10, Third Division Stuttgart Kickers five days later and Decond division Vfr Aalen on July 17.
The Bhoys take on Ajax at the Amsterdam Arena on Saturday, July 21, and Norwich at Parkhead on Tuesday, July 24.
Their SPL season will kick off against Aberdeen at Parkhead on Saturday, August 4, before a star-studded friendly against a Real Madrid side in Philadelphia on August 11.