Terry was outstanding against Italy and Hodgson expects both the Chelsea captain, and Cole, just two caps short of his century but devastated to miss a vital penalty in the shootout, to make themselves available next term.
"I'd certainly be very disappointed if they weren't (available)," said Hodgson.
"They've given me every reason to believe they're very anxious to continue.
"They were two of the real success stories of the tournament.
"I've not even thought of asking whether they will continue.
"They would have to knock me over with a feather if they came to me and said 'I'm not'."