The 18-year old winger recently rejected a contract extension offered by the Dons as he continues to be linked with a possible move to England.
Former defender McLeish spent almost his entire career at the Pittodrie Stadium and he has urged Fraser to make the most of the opportunities that come his way.
"If I look at my own career, I stayed at Aberdeen for 18 years. People ask if I regret not going down south and even though I look back and say I never regret anything, I always wonder," he told the Daily Record.
"I'm not here to say what Ryan Fraser should do. He's still a young man learning his trade but if he's good enough he's old enough.
"Players at Ryan's age should be looking to be regular first-teamers in this day and age when clubs have been dumbing down financially and there's a resurgence of kids coming through the ranks.
"From the highlights I've seen he looks an exceptional talent."