Redknapp's contract with the Hoops expires next summer, but Fernandes is keen to retain stability at Rangers following a spell of 15 managers in eight years.
Fernandes told The Guardian: "What happens if we don't win for 12 or 13 games? But I think we've made our mind up to stick – we'll just stick with Harry come what may. We want stability, we want players to know he's the manager. A different approach, I think.
"My whole life's been stability. People who have worked with me have for a long time. "I don't believe football clubs can be any different.
Redknapp took over at QPR in 2012 and led them to promotion via the Championship playoffs last season.