McCoist confirmed that he wanted the Sunderland job when Simon Grayson was dismissed, and he was given the opportunity to speak to Bain about taking the job.
The former Black Cats player said: “I spoke to Sunderland with Martin, but I did think I had a chance at the job. Sunderland are clearly a club that are close to my heart and I wish them all the very best.”
Sunderland ended up placing Chris Coleman in charge instead of McCoist, as they seek to spark a big improvement in their form.
Sunderland are currently sat at the bottom of the Championship table, after what has been a disastrous campaign to date.
The Black Cats have not been able to find the winning formula, and have picked up three points on just one occasion.
Coleman has already taken charge of his first Sunderland match, but the North East side were beaten 2-1 by Aston Villa on that occasion.
Sunderland are next in action this weekend, when they take on Burton Albion at the Pirelli Stadium.