The England international, who was linked with a move to Arsenal earlier in the summer, is not part of the vision new manager Manuel Pellegrini has at the Etihad Stadium.
City would prefer 32-year-old Barry to leave on a permanent basis but will let him go on a season-long loan if a sale cannot be arranged.
He left Villa Park in 2009 in a £12million move and has made 132 Premier League appearances for City, helping them win the title two seasons ago.
Barry was Villa’s captain and a folk hero to fans but the tide of opinion turned when the Hastings-born midfielder campaigned for a move to Liverpool 12 months before joining City only for the deal to collapse at the last moment.
He has won 53 caps for England and been a fixture in World Cup and European Championship squads dating back to 2000 so playing regular first-team football for a top flight club this season is a priority if he is to have any chance of enjoying one last major tournament in Brazil next summer.