Mikel Arteta is eager to bolster their attack during the summer transfer window and has set his sights on Sesko.
The Leipzig forward has been in top form, scoring 18 goals and providing two assists in all competitions this season.
Sesko has also favoured a move to Arsenal, which could also give the Gunners a green light for the transfer deal.
Arsenal and Sesko deal
According to The Mirror, the Gunners have taken the lead, with the Slovenian choosing to join the Emirates over their competitors.
Sesko spent four years playing for Red Bull Salzburg, where he scored 29 goals in 79 games, before joining Leipzig last summer.
His release clause was reportedly worth £43 million, but Sky Germany said that because of his stellar play, it has increased and is now estimated to be worth £64 million.
Given his age and talent, Sesko would be a long-term addition to the Gunners, and over the past month, rumours of a possible transfer to the Emirates have only grown.
Elvis Basanovic, the forward's agent, attended Arsenal's matches against Chelsea and United last season.
Leipzig had a successful season, placing fourth and earning a spot in the Champions League for the next year.
Sesko is scheduled to travel to Euro 2024, where Slovenia will be participating for the first time since 2000.