Carrick, 31, held talks with Hodgson and coach Gary Neville over the summer and has made himself available for Wednesday's friendly against Italy in Berne.
"He didn't want to be considered for the Euros so I reluctantly thought if people are not available they are not available.
"He has had discussions with Gary and me since and it turns out that he does want to play. This is an ideal opportunity to invite him to come and play for England again.
"There has never been any doubt that Carrick has not been in our thoughts or our wishes. It was more a case of believing he wasn't available for England and it was a final decision."