The Argentine aims to be back in training by next week and could line up against the Black Cats at Wembley, but Saturday's visit of Stoke City will come too soon for him.
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Aguero feels his return to first-team action is imminent, tweeting: "Feeling very good about my last week of recovery work. If I keep it up next week I'll train with the team!"
Although Saturday's visit of Stoke City comes to soon for the Argentine, City manager Manuel Pellegrini will be boosted by the return of Aguero, who has already scored 26 goals this season.
Goals from Lionel Messi and Dani Alves saw Barcelona run out a 2-0 winner at the Etihad Stadium in Tuesday's Champions League last-16 first leg, leaving the club with an uphill task to reach the quarterfinals.