Barca were thrashed 5-1 on aggregate by rivals Real Madrid in the Supercopa de Espana, with Neymar missed and Suarez suffering a knee injury that will see him miss four or five weeks.
City have already spent big this summer, signing full-backs Kyle Walker, Danilo and Benjamin Mendy, as well as goalkeeper Ederson and winger Bernardo Silva, but Yahoo Sport France believes Messi could be set to leave the Nou Camp for the Premier League.
Messi agreed a new deal until 2021 last month, but the Argentina captain is yet to officially put pen to paper.
However, Barca hierarchy are thought to have changed their mind and now want Roberto to stay and fight for his place.
"I started at the Bernabeu (in the Spanish Super Cup), the coach gives me confidence and I scored and I want to continue being an important player", he told media after the league opener.
The Swedish star, who is never shy of posting what he's up to on social media, looked in better shape than ever when he was seen kicking a boxing punch bag acrobatically in the gym on Sunday.
And while City are willing to meet the Argentine's eye-watering buy-out clause, they could reportedly try and sign him on a free ahead of next season when his contract runs out.
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