Reports yesterday said the Frenchman's agent had held talks with Neil Lennon's side.
Ciani, 28, was linked 18 months ago with a £10m move to Arsenal after he forced his way back into the international set-up.
Despite an early-season loss of form last term, he was a regular starter for Bordeaux and has played more than 100 games in three years since his £3.5m transfer from Lorient.
Although there has been interest from Newcastle United, Wigan Athletic and Seville, Celtic seem among the favourites to sign him.
Triaud said: "Would Celtic want to sign Ciani? Would Ciani be interested in moving to Scotland to play for them? Why not? It's a big club and he's a very good player, so it's a good match. We wouldn't let Ciani go for nothing but are realistic with what he is worth. Football is no longer a world full of rich clubs.
"The money has gone and all clubs are struggling, so we can't demand what we used to be able to for a player of his quality. Michael is an Anglo-Saxon-style defender, he's made for football in England or Scotland."