Carrick ruled himself out of contention for a spot in England's Euro 2012 squad due to uncertainty over his starting place, and Hodgson insists that that was the only reason behind his exclusion.
However, Hodgson has since spoken to Carrick and the Manchester United midfielder was keen to rejoin the England set-up, with Hodgson more than willing to oblige.
"Michael Carrick would have always been in our thinking. I was given to believe he didn't want to be part of the England set-up. He didn't want to be considered for the Euros so I reluctantly thought if people are not available they are not available," Hodgson told Sky Sports News.
"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."
Carrick has won 22 caps for his country, the last of which came in 2010.