All three candidates have either managed or played for Sunderland before.
Both possibilities have been mooted this week - a fortnight since Simon Grayson's sacking at the Stadium of Light.
But while Gray would not be averse to the appointment of Heckingbottom - once his Sunderland understudy - the 43-year-old told Talksport this morning (Tuesday) he'd prefer a more experienced candidate.
"Paul Heckingbottom is doing a great job at Barnsley on a shoestring," said Gray. "He’s got this philosophy at the football club where they don’t sign players over the age of 24, so is that the route that Sunderland are going to go in? Well if they are then, you know, why not give somebody like that an opportunity?
"But I still think it’s there for an experienced head, somebody like Ally and I’ve mentioned Peter Reid on numerous occasions. It’s a decent partnership, that."
Though McCoist is 15 years' Heckingbottom's senior, the Scot has little more than a year's more experience in management.
Nevertheless, the 55-year-old led Rangers to back-to-back promotions in that time, and could benefit from the assistance of someone like Reid - the former Sunderland boss whose career in management spans three decades.
Heckingbottom initially took charge of Barnsley on a caretaker basis in February 2016, but has already won one promotion and a Football League Trophy as well as having established his boyhood club as a Championship side once more.
Who would you rather see in charge of Sunderland?