Hutton enjoyed some excellent Champions League performances for Rangers this season and caught the eye playing for Scotland in the Euro 2008 campaign.
Tottenham and Newcastle have been credited with an interest in the 23-year-old, who signed a five-year deal at Ibrox in July.
McCoist saw an early career move down south, with Sunderland, turn sour before embarking on a highly successful 15-year stint with Rangers.
And the former Gers and Scotland striker added: "Alan is still young and has a bit to learn.
"With a bit of luck, he can learn at our place over the next few years."
Meanwhile, McCoist is in no rush to make the next move in his own career.
He has played down any suggestion he could be being lined up as the natural successor to manager Walter Smith.
McCoist told Rangers News: "I have no idea if this is a grooming process for me - you would have to ask the chairman that.
"I'm not trying to run here before I can walk."