The 33-year old former Heart of Midlothian, Everton and Sheffield United full-back has been training with the Dons since his contract at Huddersfield Town expired earlier this summer and Brown has indicated that he wants him at Pittodrie Stadium next season.
"I'm interested in a short-term deal for Gary but he can play for a longer one," said Brown.
"You just have to look at Hughes. He was playing out of his skin in Germany.
"I hope Gary expects the deal but we'll have to see what his expectations are."