The 22-year-old has endured an injury-plagued debut campaign with City, but returned for the last month of the season and scored both goals in the Blues 3-2 defeat by Norwich on Sunday.
Rodwell has two caps, both in friendlies, although he has not played for his country since November 2011.
Although there is no official withdrawal from Hodgson's squad as yet, it is understood Manchester United midfielder Tom Cleverley is not expected to play any part in either fixture.
Cleverley was substituted during Sunday's 5-5 draw at West Brom, although as Sir Alex Ferguson did not speak with the media afterwards, it was not apparent what the problem was.
It brings to six the number of players in Hodgson's squad who have flown out on Monday for the two post-season games between Manchester City and Chelsea.