An abject 3-1 home defeat to Southampton on Saturday left the Rs rooted to the bottom of the Premier League with just four points after 12 games, five clear of safety.
And the 62-year-old has stated that Fernandes must "bite the bullet" and sack the Welshman if his former club are to beat the drop, suggesting that Redknapp is the perfect man for the job.
"You may have to bite the bullet and say it is time for Mark Hughes to move on," Parkes told reporters.
|2/1||QPR are 2/1 with William Hill to finish bottom of the Premier League
"There is only one person who can make the decision and that is Tony Fernandes."
While Parkes, who played for the Rs between 1970 and 1979, has sympathy for the difficulties of Hughes' task at the west London club, he insists that it will only get worse for the club the longer that the 49-year-old remains in charge.
He continued: "They have some tough games coming up and if he carries on backing Mark Hughes and they keep losing it is very difficult to get yourselves out of that position.
"The longer [Fernandes] leaves it the worse it will be for a new manager coming in and unfortunately that is what they need now, a new direction.
"It is horrible when you see a manager in this position but I would think he would slowly be running out of time and I am not sure how long he can carry on in the job."