The Brazilian striker made an immediate impact after his transfer from Palmeiras was ratified in January, scoring three goals in five games and impressing with the quality of his all-round performances.
Having scored twice in the win over Swansea at the Etihad in February, he fractured his metatarsal in the following game away at Bournemouth.
The early prognosis suggested he could miss the remainder of the campaign – but Guardiola says there is a chance he will return to the squad sooner than expected.
Jesus recently travelled to New York ahead of City’s summer tour of the US and has now stepped up his recovery at the CFA.
“He was in New York. It was freezing. He told me that,” Guardiola said.
“The crutches are gone. He start to work and hopefully he will start to run and then help us in the last games of the season and then come back in the pres-season fit.”
City face Arsenal on Sunday in a crucial game between two sides chasing a top-four finish in the Premier League.
City currently sit third in the table, with Arsene Wenger’s side sixth, seven points behind the Blues with a game in hand.
And other than long-term injury victims Jesus and Ilkay Gundogan, Guardiola says he has a fully fit squad to choose from for the game at the Emirates.
“Except Gabriel Jesus and Gundogan, the others are okay,” he told reporters. “Yeah, (Pablo) Zabaleta as well (as Raheem Sterling and Kevin De Bruyne) is fit. They are not top, top perfect but, yeah, they are fit.”
