Spaniard Rafael Benitez, the former Liverpool and Real Madrid manager, was put in charge to try to recover the season but two victories in the following nine league games did not save the club.
Kevin Keegan feels McClaren should have gone earlier.
"They started the season with Steve McClaren," said Keegan. "He struggled and I guess he and the guys at the club kept thinking he would get it sorted out and he didn't.
"They left it very late and appointed Rafael Benitez and by that time you are looking for almost miracles as you need a lot of points from a few games.
"Benitez might fancy it. It is a big club. Once you go there and manage it, it does impress you as a club. The stadium is impressive, the fans and their passion is something that you can't help but like and want to be part of.
"He hasn't managed in the Championship - would that be a worry? I don't think so for a man of his experience. It might be a really good experience for him."