The R's, who are seven points from safety with seven games to play, are among the favourites to be relegated from the Premier League this term.
However, Fernandes is keen for Redknapp to remain in charge for the foreseeable future.
"I want stability more than anything," Fernandes told London Call-In.
"He has a great coaching staff and philosophy - he's a fantastic man and I would love to keep him as long as he wants to stay."
QPR resume their battle against the drop on Sunday when they host fellow strugglers Wigan Athletic at Loftus Road.