City are looking for a fee in the region of £50 million for the Brazilian international (56 caps, 19 goals) and Arsenal are the clear front-runners in the chase for the 25-year-old.
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Arsenal are currently working on the structure of a deal with a set transfer fee and bonuses that would satisfy the Premier League champions. A first offer of £30m was rejected but Arsenal will submit an improved bid.
Jesus, who has only one year remaining on his contract, wants to join the London club and he fits exactly the profile of player that Mikel Arteta, the Arsenal manager, is looking for.
Jesus scored 13 goals and gave 12 assists in all competitions for City this past season and can play in all attacking positions. He also excels at pressing and counter-pressing, which are key aspects of Arteta's playing style.
In the meantime, the Gunners are on the verge of recruiting Porto starlet Fabio Vieira. The attacking midfielder, 22, is expected in London on Friday to pass his medical and sign a five-year contract for a transfer worth up of €40m.