Andy Robinson, who Gregor assisted for three years, resigned after three defeats in the autumn Test series.
Gregor has only just started in his first head coaching role at Glasgow Warriors, and says his focus is with the Scotstoun-based club.
"My focus is firmly on Glasgow Warriors," he told BBC Scotland. "I know I have a lot of work to do to improve as a coach."
Gregor was appointed Scotland attack coach in 2009 when Frank Hadden was head coach and continued in the role under Robinson until this summer, when he took over from Sean Lineen at the Warriors.
"I'm enjoying this opportunity and I'll give it as much as I can to make the team successful.
"I've got a lot of work to do. I've been pleased with a lot of aspects of our season so far, but there is a lot if improvement to come from this group."