While Portsmouth chief Redknapp does not feel McClaren should lose his job, he accepts that the knives will be out if England do not qualify for Euro 2008.
And he doubts whether the right man would be appointed if the decision is left to FA chief executive Brian Barwick and an international committee.
"I really hope the FA are not looking for a new England manager this time next week," Redknapp wrote in his column in The Sun.
"But, if that should be the case then please let us have some real football people making the decision.
"I do not have too much faith in the FA's international committee getting it right.
"We all know there will be a huge backlash if England miss out, and history suggests that when the team fails, the manager goes.
"Then we are all in the hands of Brian Barwick and his chums to find the right man.
"With the greatest of respect, the likes of Phil Gartside, Dave Richards and David Sheepshanks have not always got it right when selecting a new manager for their clubs. So why should we trust them to appoint the new England boss?"
Redknapp has urged the FA to seek the advice of experienced Premier League bosses should they decide to let McClaren go, and has made himself available to be on the selection panel.
"They might not be English but they know exactly what is required to be a successful manager in the modern game.
"And yes, I would happily help out on such a selection panel if required. I have been around the game for long enough and reckon I could make a valuable contribution."