Reported by The Guardian, the 78-year-old hit out at Tuchel while fielding questions at the event, calling him "a German spy" before appearing to perform a Nazi salute.
Tuchel is the third foreign manager to take the helm of the England national team, winning his first two games against Albania and Latvia, scoring five goals and conceding zero.
The event took place before Tuchel's reign began, and although the former Tottenham manager appeared to be joking, his remarks have come to light.
Redknapp said: "I'll be honest with you; I think he's a German spy. I’m telling you. Seriously, he's been sent over to f*** us up. He has.
"I'm telling you, he's like Lord Haw Haw in the war – 'We have your best soldiers captured' and all that."
He then did a crude German accent, said "Ja" and raised his left arm, in what appeared to be a Nazi salute.