The Mirror says there is a feeling that Joe Hart would benefit from working with England goalkeeping coach Dave Watson.
A City move for Watson, however, would cast a shadow over the future of Mancini, because of his friendship with current City keeper coach Massimo Battara.
Italian Battara is old friends with Mancini - the pair were teenage trainees together at Bologna.
If Mancini leaves Eastlands, then Battara will almost certainly quit too.
Even if he stays, the City board could still overrule Mancini on the best way forward for Hart, who has formed a close bond with Watson since first working together, when the keeper was loaned to Birmingham City.