Redknapp's position has been in doubt in recent weeks following the team's poor start to the season, but he eased the pressure on Monday night by overseeing a 2-0 win over Aston Villa.
While QPR's place in the Premier League is far from certain, Fernandes believes that the 67-year-old is the best person for the job.
"I believe stability is the best way," he told Sky Sports News. "If you look at the clubs who have succeeded, they have had consistency in managers. Harry is my man. It is not in vogue to say that, but I stand by my manager.
"It's up to Harry whether he wants to continue as well. I hope, if he decides management is not for him next year, or the year after, or whenever, then he still has a role [at the club]."
QPR continue their Premier League campaign on Saturday with a trip to leaders Chelsea.