The 18-year-old winger is regarded as one of the best young players in Scotland and his performances have reportedly attracted the attention of a host of Premier League clubs.
However, Brown has vowed to do "everything" to keep the talented midfielder at the Scottish Premier League club.
"We will be doing everything in our power to keep Ryan. That's all I can promise fans at this stage. He plays with maturity which is why he has come through so strongly," Brown told reporters.
"Look at what happened to Fraser Fyvie, who went to Wigan and never features in their matchday 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."
Aberdeen currently sit third in the SPL.