Beale was credited with performing a key role on the training pitch under Steven Gerrard as Rangers clinched the Premiership title in an unbeaten 2020-21 league campaign as well as reaching the Europa League last 16 on two occasions.
The 42-year-old followed Gerrard to Aston Villa last November but went his own way at the end of last season, taking his first steps into management when he took over the reins at Queens Park Rangers.
Beale made a flying start at Loftus Road and was sitting top of the Championship early on, but no wins in their last five league games before the break saw the Londoners drop to seventh.
Rangers are looking for a new head coach after Giovanni van Bronckhorst’s sacking was announced on Monday morning and Beale has been installed as the frontrunner among bookmakers.
QPR director of football Les Ferdinand has insisted he will not stand in the way of an approach from Rangers as long as compensation terms were met, reported to be in the region of £1.5million. Beale was offered the Wolves job last month but turned down the chance to manage the Premier League side.
McCoist, however, expressed concerns that, just four months into his managerial career, Beale might be too inexperienced to take over the “massive job” at Rangers.
Discussing the managerial vacancy on talkSPORT, McCoist said: “Excellent reports about Michael as a coach, is it just a little bit early? I'm not sure. I'm really not sure. Do you go for more experience? Someone like Sean Dyche or one or two others.
"Michael Beale is certainly very well thought of, but I'm not sure if it's maybe a little bit early because it's a massive job. The pros are he knows the place, he's been there before, the players know him and he's had a better than reasonable start to his managerial career at QPR, although they have dipped a little bit, losing four of their last five."
Steven Gerrard has also been linked with a potential Ibrox return but Rangers’ all-time record goalscorer - who also managed the club during their ascent from the lower leagues following liquidation in 2012 - does not see that happening.
McCoist added: "I am pretty open minded, I'm eager and keen to find out who the replacement will be. There is no real standout candidates, I think it is pretty open between four and five.
"I don't think that will happen (Gerrard return), I wouldn't say burnt bridges, far from it, I would say the vast majority of the Rangers support were delighted with the job he did winning that big title, but I think there is one or two who are not happy the way it ended and I think it would be tough to come back from that."