The West Brom boss will formally begin his involvement with the England team after the final round of Premier League fixtures this Sunday, when the Baggies take on Arsenal.
Hodgson will name his squad for the forthcoming tournament next Wednesday, and has a dilemma to solve up front with star man Wayne Rooney banned for the first two group matches after being sent off in the final qualifying game against Montenegro last October.
|Hodgson to name England squad on May 16
The former Liverpool boss has a variety of attacking options to choose from, but Dublin believes that the 64-year-old should turn to Crouch - who has not been selected for the national side since the friendly with France in 2010.
Dublin told Press Association Sport: "My first choice striker would always be Wayne, but away from him it would always be Peter Crouch because people just do not know how to mark him.
"Crouchy is not the kind of person who would cry because he is not being picked, he would always put himself in the frame to be.
"His record is better than anybody else's as a striker in terms of games to goals for England, so on that basis I think he should go."
Dublin, who won four England caps, has also been impressed with the late-season form of strikers Andy Carroll and Grant Holt and feels that this has left Hodgson with a pleasing selection problem.
He continued: "Andy Carroll has raised his level in the last two or three games, Grant Holt is always going to be a handful, so is Bobby Zamora. There are a lot of good strikers. It will just be about picking the right ones who are in form.
"In the end, it will be down to the manager's choice of style. Roy normally likes a big man and a small man, which might make his decision to take Carroll or Crouch."