Dyche has steered the Clarets up to seventh place in the table, and his opposite number at Palace has taken note of the "excellent job" he has done at Turf Moor.
"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," Sky Sports News quotes former Three Lions boss Hodgson as saying.
"Why shouldn't a guy like Sean Dyche be in that group of people to be considered. I see no reason why anyway."
Palace play host to Burnley in the Premier League this weekend.