In the wake of the Hoops' Champions League last-16 exit on Wednesday night at the hands of Juventus in Turin, the prospect of the Northern Irishman attracting interest from other clubs on the back of such an impressive run was acknowledged by chief executive Peter Lawwell.
Even Hoops keeper Fraser Forster, when asked about his manager possibly moving on, said he "could definitely see it happening."
However, ahead of tomorrow's SPL clash with Ross County in Dingwall, the Parkhead boss said: "It (speculation) makes no difference to me.
"I am the manager of Celtic and I am one of the privileged few who have been lucky enough to do this job. I enjoy it, I love what I do.
"I can't stop speculation about players or myself but at this current period I am Celtic manager and I don't see any reason for that to change in the future.
"Does it flatter you? It just means that you might be doing a decent job along the way.
"But why are we talking about me leaving Celtic all of a sudden?
"I am only three years into the job. I am doing my job, I haven't done a job.
"I want to improve myself, the team, the players and take the club forward.
"We have made huge strides this season. It is going to be difficult to replicate it next season but that is the challenge that lies ahead."