Arsenal are in the market to sign at least one forward and have sounded out the 25-year-old over a possible move.
Initial contact has now been made between the two clubs and sources have told ESPN that Arsenal have baulked at City's valuation given he only has one year left on his contract.
However, the amount is based on City's respect for the player -- who has scored 95 goals in 235 appearances -- but also a desire to recoup the €60m fee paid to Borussia Dortmund to sign Erling Haaland.
City boss Pep Guardiola would prefer to keep Jesus but will not stand in the striker's way if he pushes to leave.
Jesus has started 20 Premier League games this season and has previously hinted at his frustration at not being more regularly involved.
Jesus' agent Marcelo Pettinati confirmed to the Guardian last week that talks had taken place and "we like the project" but also that there were six clubs in the frame.
That will make a deal for Jesus harder to pull off, although not impossible.
Arsenal will wait to see what European competition they qualify for this weekend before deciding their next move but sources have told ESPN that Arsenal did not expect to finish in the top four this season and therefore their long-term budgeting has not been significantly affected by the recent slump.
Whether they pursue a deal for Jesus remains to be seen. Head coach Mikel Arteta is a huge admirer of the player having worked with him at City but Arsenal are looking at other options including Paulo Dybala, who will leave Juventus on a free transfer at the end of the season.
Arsenal have made contact with Dybala's representatives to find out what personal terms the player is seeking.
Sources have told ESPN that a member of Dybala's entourage held meetings in London and Manchester before flying to Spain and Italy for similar conversations as Dybala assembles his options before making a decision on his next club in the coming weeks.