However, the Gunners will face stiff competition in the race for the 26-year-old as Liverpool are also keen.
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Paris Saint-Germain have been linked too, but Arsenal are hoping their offer will be enough to tempt the Serie A club into doing business with them.
Atalanta value Lookman at around €70m and are already thinking of handing the Nigeria international an improved deal which would see him earn €3.5m per season.
The former Everton star ended last term with 11 league goals and seven assists in 31 appearances, helping his side clinch the Europa League by notching a hat-trick in the final against Bayer Leverkusen.
A return to England could be appealing to the Charlton Athletic academy graduate, and joining Arsenal could be an option he prefers after watching them challenge for the Premier League title over the last two seasons.
Kiwior is currently surplus to requirements at the North London club after they tried to include him in the deal which saw them sign Riccardo Calafiori.
The Poland international was left out of the matchday squad that faced Wolverhampton Wanderers in their opening Premier League game of the new season, and he could now come in handy in their pursuit of Lookman.
The Wandsworth-born forward can play on the left wing, as a number 9 and behind the striker, and Arsenal manager Mikel Arteta admires such a versatile attacker.
Bolstering his options in the final third has always been part of the plans of the Gunners boss this summer, and it appears he has finally got the perfect option.
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