Scottish Rugby chief Mark Dodson doesn't expect Dominic McKay to join Celtic before his expected start date of July 1 despite Neil Lennon's exit.
The Murrayfield chief operating officer will replace outgoing Peter Lawwell in the summer and faces a mammoth rebuilding job.
A new manager will be needed and a director of football also expected to be identified ahead of next season.
Celtic don't have their problems to seek with a host of players set to move and the challenge of wrestling the title back from Steven Gerrard and Rangers.
But SRU head honcho Dodson expects his key man to remain amid the ongoing Six Nations campaign and beyond.
He said: “What's happening at Celtic is out of my control. It's not something I'm utterly familiar with but I do know Dom is going to have a very full in-tray when he gets there.

"The issue for us is that he has a notice period that he has to serve here and we need stability in our business too. So I expect Dom to be here with us for a while."
Dodson's words come hot on the heels of Brendan Rodgers insisting his former club would be best served in finding a football specialist to work alongside McKay.
He said: “At the highest level, in particular, it's a role which is very important. I think in the modern game, it's absolutely critical to have that.
“Obviously the manager has to be able to bring in players he wants because he's accountable for what happens on the pitch. I'm pretty sure that's something Celtic may be looking at."