Manchester United midfielder Cleverley played in the Red Devils’ dramatic 5-5 draw at West Brom on Sunday but the FA confirmed he is unlikely to be able to feature in the two friendlies.
Rodwell, meanwhile, bagged a brace in City’s 3-2 defeat at home to Norwich and will join up with Roy Hodgson’s squad, which will first face Giovanni Trapattoni’s men on May 29 at Wembley Stadium.
The 22-year-old Rodwell has two England caps but hasn't featured for England since November 2011 after failing to make a significant impression at City since his 12 million pound move from Everton, but his brace against the Canaries has filled him with confidence.
"It's a little bit bittersweet,” Rodwell told City TV after the game on Sunday. “The result wasn't what we wanted, we wanted to finish the season on a high.
"On a personal note, it was good to get on the scoresheet. I've been unlucky in the last few games not to.
"Luckily they managed to go in and hopefully next season there'll be a few more.
"I've missed a lot of games this season. It's hard for me to come back and just feel 100 percent. I feel like I need games, back-to-back games. I'm sure that'll bring the best out of me."