Strachan was confirmed as Craig Levein's successor on Tuesday and will cast his eye over the nation's top talent before selecting a squad for next month's friendly against Estonia at Pittodrie.
Ian Black is the only Rangers player to receive a call-up since the club was demoted to the bottom-tier of Scottish football, but Lee Wallace has previously played for his country and David Templeton has been in fine form for the Light Blues.
McCoist has welcomed the appointment of Strachan and hopes he will be open-minded about the possibility of picking some of his players.
He said: "I'm certainly not going to attempt to tell him how to pick his squad or his team.
"What I would say is, I think if our players deserve to be in the international squad, I don't see any reason why Gordon wouldn't pick them. I'm sure he would.
"I'm delighted. Eventually we have Gordon in charge. He was the man for the job for the majority of people.
"I know Gordon reasonably well and I think he will do a great job. I'm very hopeful that Gordon can get us back on track.
"I don't think he is hungry because he has been out of the game for two years - I think Gordon is generally a hungry character in terms of wanting to do well and wanting to succeed.
"That won't have changed, I wouldn't have thought.
"I know Gordon keeps up to speed with football all over the place and he's been to games during his time out of management. It certainly won't be a problem."