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Green was dropped for the Lincoln game earlier this month and was fined two weeks' wages for not turning up to watch and instead being a spectator at Brunton Park for Carlisle's game with Kidderminster.
He has indicated that he wants to return to his home-town club - whom he played for on loan two years ago - despite recently signing a 3½-year deal with City.
Tigers chairman Adam Pearson said he "only wants players who are fully committed to the cause and if Stuart Green sees his future at Carlisle then that is where he should play."