This is not the first time that City have been linked with the Argentine forward, though Chelsea and Manchester United have also shown an interest.
Italian media suggest Manchester City came forward with a proposal worth €22m, but that Roma shot it down without any consideration.
The Giallorossi are rebuilding and do not want to lose their most consistent young player.
He just turned 21 last month and has scored 14 goals in 28 Serie A games this season.
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