The most capped French player ever is now out of contract, after leaving Chelsea and retiring from International football.
He said today, "I would like the chance to play for Celtic, if they want me, because I have watched them over the last couple of years and I like the way they play.
"I also know about Martin O'Neill and I believe I could work with a manager like him.
"At this stage in my life it's about wanting to play with another big team with high ambitions because I know I have at least one, maybe two good years left and I think Celtic would be ideal.
It is unlikely that Celtic are even remotely interested in the 35 year old, and this is a move by Dessailly to let clubs know he is available.
We are not a retirement home, unlike our friends across the city, but with Dessailly's experience and ability, he could be a decent addition to the squad for next season.
As now, though, the story is 100% speculation.
"They are in the Champions League, they want to progress and I could help them do that."