Expectations from the Brazilian forward were cooled by Arsenal manager Mikel Arteta ahead of Friday's Premier League opener at Crystal Palace, saying the striker still needs time to settle in.
During the preseason, Jesus has scored seven times in five games, having scored 95 goals in 236 appearances in all competitions and played an important role in Manchester City's four Premier League-winning seasons.
"The role that Gabi has here is going to be very different to the role in his previous club. That needs some adaptation and some time," Arteta said, who worked with Jesus during his time as assistant coach of Pep Guardiola.
"When you bring top players from top clubs and they have been extremely successful over the years, they are going to expect that... He is an enormous talent, a player with a mentality that is so contagious and he is going to give us a lot.
"He has done fantastically well and we are all surprised at how quickly he has done it, but we have to share that responsibility."
Arsenal have been very active during this transfer window bringing in Oleksandr Zinchenko, Fabio Vieira, Marquinhos and goalkeeper Matt Turner.
Arteta indicated there could be room for more arrivals before the transfer window closes on September 1.
"It's always been my team. We have changed the squad," Arteta said. "The players we have are more specific and better to the way we want to play.
"We are really active as you can see with ins and outs. Everything is still open, it's a long window... Players are going to have the need to leave, some others to move and everything is open still."
Left-back Kieran Tierney is still making his way back after a knee surgery in April while right-back Takehiro Tomiyasu and new signing Vieira have not featured during pre-season due to injuries.
Reports suggested that No. 10 Emile Smith Rowe is still nursing a groin injury and will not travel to Selhurst Park.
Arteta said he hoped three of those four players will be training later on Thursday and could be in contention to face Palace but declined to specify who would miss out.
Palace, managed by former Arsenal captain Patrick Vieira, beat Arsenal 3-0 in April last season but Arteta was more optimistic about Friday's trip to south London.
"They showed last season how tough they are and how difficult they are to beat and how consistent they were at home as well... Hopefully, we learnt a lot of lessons that day," Arteta said.