Millen has been in charge of the Premier League strugglers on a caretaker basis since the departure of Ian Holloway last month.
A number of managers have been linked with taking the vacant post, including the likes of Aitor Karanka, Chris Coleman and Malky Mackay, but the Palace hierarchy are yet to decide on Holloway's permanent successor.
However, Browett feels that "top guy" Millen deserves the chance to remain at Selhurst Park when an appointment is made, although he confirmed the make-up of the new boss' coaching team will be entirely their decision.
"He (Millen) is a Palace supporter and his dad played for Palace," Browett told the Croydon Advertiser.
"He has got the support of the players and the board and he has done a very good job. When we appoint a new manager it will be down to him who is in his backroom staff.
"We are not naive enough to think that we can tell the manager how to run his club – we may be the owners of the club but we are not experts in running a football team and that is the manager's job.
"He will choose his backroom staff, but if he does have a place for Keith, I would love that."
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