Rooney made his playing debut for Derby County in a 2-1 victory against Barnsley on Thursday night, and a reunion with Hodgson is on the cards as the Rams prepare to take on Crystal Palace in the FA Cup third-round on Sunday.
The former Manchester United forward was made England captain in 2012 during Hodgson’s time as England manager.
The Englishman believes Rooney still has plenty to offer as a player, but once he retires, he should follow the lead of Lampard and Gerrard, who are currently relishing their moment at Chelsea and Rangers respectively
"We have seen two other players of the same generation,” he said.
"I gave Wayne his 100th cap, Steven Gerrard and Frank Lampard both earned their 100th caps playing for England during my time there.”
“Steven Gerrard and Frank Lampard are making a hell of a go of their management careers so why shouldn't Wayne be included in that?
"He is a leader type – there is no question of that.
"All three of those had leadership qualities that they were able to show on the field of play.”
“That is what the real good leaders are. It is not just a question of talking a good game or being persuasive verbally, it is a question of being able to get on the field of play and show leadership qualities when you need them."