The Gunners are primarily targeting a centre-forward this summer after Pierre-Emerick Aubameyang left in January and Alexandre Lacazette’s departure was confirmed when his contract expired at the end of June.
Jesus, who has just one year left on his contract with City, has been heavily linked with a move to the Emirates Stadium.
The Brazil international’s playing time has been limited as the striker was also used in a variety of positions in City’s attack last season.
With Erling Haaland arriving in the summer, Jesus’ minutes would be cut even further should he stay at the club.
Arsenal will be without Champions League football next season after narrowly losing to Tottenham in the race for the Top 4.
Burley has questioned whether Jesus can be fully convinced of a move at Mikel Arteta’s side.
“It’s tough. You need to attract players who are sure to fill that position. They have some youngsters who have filled the broader positions and [Martin] Odegaard at the back,” Burley told ESPN FC.
“I think if I were Jesus I would be more inclined to sit and wait, especially if there is a year left. Whether Man City are trying to dissuade him by suggesting there won’t be many minutes of game time [next season], I do not know. Of course, the squad is strengthened by some new signings.
“It’s difficult for the player because he’s good enough to go somewhere and become that forward again that we know he is. He has been used in many positions and has done a good job.
“It’s about if you could persuade him to go to Arsenal, where is it just about the project?
“At the end of the day, Arsenal are a long way from contending for major accolades.”
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https://metro.co.uk/2022/06/08/manchester-citys-gabriel-jesus-sent-warning-over-arsenal-transfer-16790804/ Manchester City's Gabriel Jesus warned against Arsenal transfer | Soccer