According to Football Italia, the Gunners are ready to pay €50m with Jakub Kiwior as part of the deal.
Lookman has been linked with Paris Saint-Germain in recent weeks, but it appears the interest of the Ligue 1 champions has cooled off.
The Super Eagles winger played against Real Madrid in the UEFA Super Cup last Wednesday, but asked to be left out of their Serie A opener against Lecce on Monday.
Lookman was not in training on Wednesday either and Sport Italia transfer expert, Alfredo Pedullà, insists that it is because he refused to participate.
The report said Arsenal have come with a bid worth €50m plus bonuses, although Kiwior could be included to lower the fee, possibly even on loan with option to buy.
Atalanta are still hoping to keep the 26-year-old and are prepared to double his current wages, after he scored 17 goals with 10 assists in 45 matches last season.
