Redknapp brought Sherwood to Spurs during his time in charge.
He told talkSPORT: "He knows the people he works for want Champions League football. If he doesn't get it he's going to be under the cosh.
"He could be a fantastic manager for Tottenham though. Whether they finish fourth or fifth isn't suddenly going to make him a great manager or a bad manager.
"He needs time and, if they give him that, then they'll have an excellent manager for the future. Why not stick with a young English boy who's come through [the ranks]?"
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