Marcel said "Chelsea have been fantastic with me by freeing me from the final year of my contract, since when I've given myself 10 days to decide what my future will hold.
"I am currently reflecting on opportunities, knowing that two possibilities are open to me. Either I can turn the page and begin a new life professionally - besides Chelsea have opened a door for me in that sense - or I can extend my playing career.
"I am flattered to note that my name has not been ignored by certain clubs. A number of Premiership clubs want me to sign but I don't want to play against my old club.
"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," Desailly added.
"I also know about Martin O'Neill and I believe I could work with a manager like him. They (Celtic) are in the Champions League, they want to progress and I could help them do that."