Poyet has been linked with Tottenham this year.
Redknapp wrote in the Daily Mail: "My spies tell me Diego Poyet, son of Gus, was excellent in Charlton’s U18 2-0 win at West Ham. A driving central midfielder, this dynamic junior England player can pass, tackle and create a tempo to a game.
"Lots of bigger clubs know of him, Charlton have done well to nurture him. I’m very keen to follow his progress."