Coppell - the Royals' most successful manager - left in the aftermath of the play-off defeat by Burnley last week and Madejski is determined to get the right man.
He said: "I make no secret of it, getting the right manager is crucial and that's why we will do things correctly.
"We won't rush, we will take due process to do it.
"We are in a very good position and I don't see the wheels coming off but it is fundamental we appoint the right manager.
"This next appointment is crucial and that's why we take it seriously."