The Daily Mail are claiming that Carrick will play alongside Steven Gerrard in place of Frank Lampard after the Chelsea man's lacklustre performance against Montenegro on Friday night.
Carrick has started three games of this qualifying campaign - a home cruise against San Marino and away draws in Poland and Montenegro. His last England caps came against Ireland and Brazil at the end of last season.
Hodgson hinted in his press conference on Monday that he was open to the idea of change in central midfield, where he also has Jack Wilshere available.
"They were all in contention for the first game and they will be for this game," said Hodgson. "I am blessed with some fantastic players in that part of the field.
"Steven and Frank did exceptionally well in that position and in Carrick and Wilshere we have two other first-class players."