"He has done an excellent job and is getting the credit he deserves," Hodgson said.
"He has built up a very good team and over the last couple of years he has got that team playing well and getting points in the Premier League."
When asked if Dyche should be considered for the role, Hodgson said: "Of course, why not?
"The job of an England manager is not confined to certain people, it is confined to who the FA believe is the right person to do the job.
"Why shouldn't a guy like Sean Dyche be in that group of people to be considered.
"I see no reason why anyway."