The Three Lions boss won widespread plaudits for picking a youthful-looking squad with an average age of 26, and the likes of Raheem Sterling, Luke Shaw, Adam Lallana and Ross Barkley all head to Brazil as international novices, but in form after impressive seasons.
Writing in his column in The Mirror, Savage said: "If Frank Lampard and James Milner start, I would not be surprised to see them in the side to face Italy in the World Cup opener on June 14.
"I would be even more surprised if they finished the tournament in Hodgson's first-choice team.
"My best guess is that Hodgson will play Lampard and Milner instead of Jordan Henderson and Sterling in a safety-first move to avoid defeat in England's first game."
England play Italy on June 14 in their opening group game, before meeting Uruguay and Costa Rica.