The ex Bristol City defender feels he can play at a higher level than League Two and new manager Dennis Wise has said he won't stand in his way.
Brown has already turned down a move to Brentford, and is now training with Doncaster Rovers.
Wise said: Aaron came to see me a while ago and he had made up his mind. He felt he could player at a higher level and get a move away. I won't stand in the way of any player who doesn't want to be here"
Wise also said if he does leave then it would be on a free transfer, although they would put a clause in his new contract that if his new club gained promotion then Swindon would get a fee for him.