The 31-year-old's last international appearance came in November 2010 during the 2-1 friendly defeat to France at Wembley.
"I did try to sign him at Fulham and I selected him for the Euros as well," said Hodgson.
"He was on a standby list but he made it clear that, unless he was in the squad, he didn't want to be considered.
"I'm not going to bring him in to fill up the bench."
Crouch has been capped 42 times at senior international level, scoring 22 goals.