The Slovenian, 20, has impressed in recent weeks for the Bundesliga side.
Benjamin Sesko has impressed for RB Leipzig this term
Sesko moved to RB Leipzig last summer and has since scored 13 goals in 30 German top flight appearances.
According to the Telegraph, Arsenal possess a "strong interest" in the 6ft 5in forward.
They add that other interested parties now believe that the Gunners are in "pole position" to seal Sesko's signature.
The former RB Salzburg ace previously had a £43million release clause built into his contract.
That figure is now understood to have risen to £64m given his red-hot recent form.
Sesko has scored in each of his last six appearances, including a goal against Champions League finalists Borussia Dortmund.
His agent Elvis Basanovic was in attendance as Arsenal beat Chelsea 5-0 last month.
Manchester United have also shown an interest in Sesko, as they seek support for Rasmus Hojlund.
Basanovic posted a snap of himself at Old Trafford for United's clash with Arsenal last Sunday.
AC Milan have also been linked with making a swoop for Sesko, with forward Oliver Giroud leaving for LAFC.
The Gunners have found success during the second half of the season playing Kai Havertz as a striker.
This has made their need for a forward less pressing, but they are still expected to enter the market for one this summer.
In addition to Sesko, they have also been linked with Viktor Gyokeres and Joshua Zirkzee.
Mikel Arteta's men are set to perform a huge clear-out this summer.
Fringe players including Eddie Nketiah, Emile Smith Rowe, Aaron Ramsdale and Reiss Neilson could all depart.
While Kieran Tierney, Albert Sambi Lokonga and Nuno Tavares, who have all been out on loan this term, are expected to leave on permanent transfers.
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