According to the Daily Mail, Guardiola is keen to bring the Argentine goalkeeper to the Etihad Stadium after he impressed on a two-year loan spell in Spain with Real Sociedad.
Hart has been targeted by Everton but it would take a massive offer for him to leave City anytime soon.
If he happens to stay, and Ter Stegen remains at Camp Nou, Pep is likely to lure Rulli from Uruguayan club Deportivo Maldonado ahead of Barca and Valencia who are also showing interest.
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