The 39-year-old won two Premier League titles during his time with Chelsea. It has been reported that the Bhoys are looking to sign him as a manager for the Under-20 side.
In September, Shaun Maloney left the Under-20 coaching role at Celtic to focus on his job at the Belgium national football team.
Duff knows Brendan Rodgers from his time at Chelsea, and he will be a smart appointment for the club. He is currently coaching the Shamrock Rovers Under-15 team.
Celtic are a big club and the job will be challenging for him. However, it is also a good opportunity for the former Republic of Ireland international to take his coaching career to the next level.