Rangers sacked Michael Beale on Sunday night following their 3-1 loss at home to Aberdeen on Saturday.
Steven Davis has been given interim charge of the club with former Rangers star Alex Rae coming in as his assistant.
Former Rangers striker Miller stressed that it is vital that Rangers get the next appointment right and they in fact bring in someone who has the character and personality to handle the pressure and expectations of managing the Glasgow giants.
He pointed out that Davis and the current management do not have the required experience and while Miller does not want Rangers to rush in someone, he insisted that they need a new manager in place as soon as possible.
The Rangers legend told Sky Sports Scotland: “This next appointment is really important for this board and that they get the right guy.
“They need someone with a proven track record of having some kind of level of success and for me more importantly, they need someone with the personality and character to stand in front of the 50,000 fans every week.
“Even when if it’s not going well, fronting up and having the broad shoulders to take the responsibility of managing this football club.
“It’s a big few weeks coming for the board because what I would say is they don’t want to rush it and make a kneejerk appointment.
“But what has happened is that Steven and the management team are very inexperienced so it’s coming to a big moment.
“They have got the international break so they have a little bit of time to do the work but the season is not lost, it can be salvaged.
“What I would like to see is the right appointment as soon as possible.”
Former Rangers defender Kevin Muscat is reportedly keen on having a conversation with the club about their managerial vacancy.