The England international has failed to make a real impression on the City first team since arriving at the club from Everton in the summer of 2012.
He has started just seven league games in the past two seasons, and just one of those came last season while internationally, he has played just six minutes for England since making his switch to the Etihad Stadium.
The 23 year old has three years remaining on his current contract, leaving the Premier League champions in a strong position regarding any negotiations.
Despite Rodwell being surplus to requirements, Manuel Pellegrini may be keen to keep hold of him as to fall in line with FA rules on home-grown players.
City begin their title defence at Newcastle United next month, and they can be backed at 4/6 to take all three points.