Cole has been a mainstay of tournament football for England since 2002, but he is no longer first choice at Chelsea. Although Hodgson says he still "retains faith" in the player, the England manager dropped a hint that Shaw will get his chance to impress on Wednesday.
When asked whether the 18-year-old Southampton left-back would play some part in the friendly against the Danes, Hodgson said: "It is a logical thought but I can't make promises.
"I think everyone who has watched him play recently will not deny that he deserves a place in a large squad like this.
"It would be nice if he gets to play on Wednesday night, but that decision hasn't been made."
Speculation had been rife that Adam Johnson, or Wilfried Zaha, would be recalled, but neither made the cut for the Denmark game.
Fit-again West Ham striker Andy Carroll was another notable omission. Hodgson insisted those players still had a chance of making his World Cup squad, though.
"This is not a definitive list," Hodgson added.
"The fact someone is on this list does not say he will be going or be one of the seven standby players because I reserve the right to change my mind on those subjects."