The goalkeeper, who made 125 appearances for his country, wants the Tottenham Hotspur boss to be appointed before this summer's European Championships.
"Harry would be my choice if it was an English manager. I think his time is now," Shilton told Sky Sports News.
"I know Spurs have had a dip in form but I think Harry is going to get them playing the right way and he'd probably get the players' respect. He has all the players in the country and he will pick players that will play football and entertain the public.
"The fans deserve to get a man in charge before a major tournament because you only get two - European Championships and World Cup - and the fans want us to do really well and so they should."