The 21-year-old, who hit a hat-trick in the 6-0 Scottish Cup win over East Fife, is near the end of his contract.
"We have asked Willie Miller (Aberdeen's executive director) to see if we can keep him, which is of course a financial issue," explained Brown.
"I think, if Chris is enjoying his football and the team is doing well, he is more likely to stay."
Maguire bagged his three goals in the first half as the Dons opened up a 4-0 lead before the interval.
"Chris has been exceptionally good recently," added Brown. "He has an eye for goal, good control and pace - every attribute you require for a striker - so it doesn't surprise me to see him scoring goals.
"He is out of contract at the end of the season and it is no surprise that clubs are taking an interest in Chris Maguire.
"In all honesty, though, I don't think we can compete with the Championship clubs in England financially, so I can only hope that we can give him the best offer we can."