Key target: Arsenal are pushing to sign a new striker this summer
Arsenal Football Newsletter
The club are long-term admirers of Sesko and tried to sign him a year ago, but he decided to sign a new contract with Leipzig.
Arsenal have returned for the 22-year-old, though, and Standard Sport understands talks have taken place with Leipzig.
The German club are willing to sanction a sale this summer, however they want a fee in the region of £70m.
Sesko scored 13 goals in the Bundesliga last season, while he also chipped in with five assists, too.
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Leipzig finished seventh in the Bundesliga - missing out on European football for next season - which has boosted Arsenal’s chances of landing Sesko.
The Gunners have looked at other striker targets, including Aston Villa’s Ollie Watkins and Sporting star Viktor Gyokeres.
Arsenal tried to sign Watkins during the January transfer window, but their bid of £40m was rejected.
Arsenal finished last season with 69 Premier League goals, which was 17 less than champions Liverpool.
Injuries played their part in that and the Gunners were without Bukayo Saka, Kai Havertz and Martin Odegaard for extended parts of the season.
Mikel Arteta, however, has also stressed the need for Arsenal to add more firepower to their squad this summer.
“Well, what we have, what is clear as well with the amount of injuries that we had in the front line, that we need a goal threat and we need the firepower out there,” he said in May.
“Understanding that the context can change tomorrow, you know, and we cannot rely just on the numbers that we had before.
“And we have to add goals, we have to add creativity, we have to add numbers and that will be in different positions.”