The Gunners forward is now into the final year of his Arsenal contract, with the North London club open to letting him go, if they receive an acceptable transfer offer in the coming days.
The Brazil international is frustrated by his lack of game time at the Emirates Stadium and wants to move on to reignite his career.
Jesus has not featured in the matchday squads for Arsenal's two opening games of the 2026/27 season as the Gunners have secured back-to-back 3-0 wins over Manchester City and Coventry City in the FA Community Shield and the Premier League.
The 29-year-old is on the radar of several Serie A clubs, with Napoli rumoured to be the frontrunners to complete a potential deal, but Jesus' preference is to remain in England.
That has caught the eye of Everton, as David Moyes looks to bring in a recognised goal scorer, alongside the inconsistent Beto and Thierno Barry for the new season.
Jesus' contract situation means Arsenal want to secure a quickfire sale and Everton are prepared to match their £20M valuation.