It means the Foxes are already on the lookout for their third manager of the season, with Frank Burrows acting as caretaker manager and Taggart his assistant.
"I have had no contact whatsoever from Megson about joining him at Bolton, and even if I had I would not go there. I am not interested," said Taggart.
"I am happy here at Leicester and I am over the moon that I have been given an opportunity to coach here. I do not want to go anywhere else. I want to stay here.
"Gary leaving means this is the start of a new era for the club. It is another page in the club's history and I want to be part of that."