The 18-year-old's performances on the wing have drawn praise and almost inevitably speculation linking him with a move south of the border.
Aberdeen legend Willie Miller saw Fraser at close quarters as the club's director of football development and has said:
"It is frightening to think what he might accomplish in the game."
However, Brown has warned that a move to the Premier League may not be in Fraser's best interests, citing the example of ex-Don Fraser Fyvie of a move that he feels has not paid off.
"We will be doing everything in our power to keep Ryan," declared the former Scotland boss.
"That's all I can promise fans at this stage.
"He plays with maturity which is why he has come through so strongly.
"Look at what happened to Fraser Fyvie, who went to Wigan and never features in their match-day squad.
"Would you be better in front of 10,000 at Pittodrie like Ryan or be like Fyvie playing on the Wigan training ground?
"I hope he can see the bigger picture and doesn't go for short-term gain."