Recent comments suggested Rodriguez could be close to a call up but instead Pearce has opted for Nathan Delfouneso, Scott Sinclair and Danny Welbeck as his front players.
Cork, whose caps to date have all been as a substitute, will be hoping to get his first start for his country.
The full squad is:
Goalkeepers:Frank Fielding (Blackburn), Jason Steele (Middlesbrough)
Defenders: Ryan Bertrand (Nottingham Forest*), Martin Kelly (Liverpool), Michael Mancienne (Wolves*), Micah Richards (Manchester City), Chris Smalling (Manchester United), Kyle Walker (QPR^), Ben Mee (Manchester City)
Midfielders: Marc Albrighton (Aston Villa), Tom Cleverley (Wigan~), Jack Cork (Burnley*), Henri Lansbury (Arsenal), Josh McEachran (Chelsea), Fabrice Muamba (Bolton), Jack Rodwell (Everton), Danny Rose (Bristol City^)
Forwards: Nathan Delfouneso (Aston Villa), Scott Sinclair (Swansea), Danny Welbeck (Sunderland~)
* - currently on loan from Chelsea
~ - currently on loan from Manchester United
^ - currently on loan from Tottenham