The 22-year-old has two caps to his name - both in friendlies - but has not played for his country since November 2011.
Rodwell, who moved to the Etihad from Everton for £12m in August 2012, scored his first two goals for Manchester City in their 3-2 final day defeat by Norwich on Sunday.
He has missed much of this season because of a series of hamstring injuries, limiting him to just 15 appearances.
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.
England face Giovanni Trapattoni's side at Wembley on 29 May and then World Cup hosts Brazil in Rio on 2 June.
Goalkeepers: Ben Foster, Joe Hart, Alex McCarthy.
Defenders: Leighton Baines, Gary Cahill, Ashley Cole, Phil Jagielka, Glen Johnson, Phil Jones, Joleon Lescott, Kyle Walker.
Midfielders: Michael Carrick, Tom Cleverley, Frank Lampard, James Milner, Alex Oxlade-Chamberlain, Theo Walcott, Jack Rodwell.
Forwards: Andy Carroll, Jermain Defoe, Wayne Rooney, Daniel Sturridge, Danny Welbeck.