Redknapp says Michael Carrick should be given the job instead.
The former United midfielder has been in charge as caretaker after Ole Gunnar Solskjaer was fired a week ago, but is expected to be replaced by the German.
"The fact United have brought in Ralf Rangnick as an interim to replace the interim, before they get the man they really want, is ridiculous," Redknapp wrote in his column in The Sun.
"I've never heard anything so stupid in my life, whichever way you look at it.
"If they wanted Mauricio Pochettino, as we were led to believe, then there were ways and means to make it happen now.
"And if they had to wait for him, they shouldn't have pushed Michael aside and put someone above him for a few months. What does that say? We've got no faith in you?"
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