Neil Lennon was left shocked by the racist abuse directed at Kilmarnock manager Alex Dyer in a letter.
Killie are working with Police Scotland to identify any individuals involved in sending the letter to the Rugby Park club following the 2-1 home defeat to Livingston on St Stephen's Day.
The Ayrshire club condemned the "disgusting act" and Celtic boss Lennon was supportive of Dyer.
He said: "Alex is one of the best football men I know up here.
"I think it's shocking in this day and age that a guy of his calibre and standing has to put up with any sort of racism at all.
"I know him personally, he is one of the best. I want him to succeed at Kilmarnock as much as anybody else.
"I think he is a great football guy and I think he is good for the game here. We want this eradicated.
"Kilmarnock have come out and supported him very strongly, which is brilliant to see, and he has our full support from everyone at Celtic."