The 21-year-old has had a fine campaign with RB Leipzig. He has registered 19 goals and provided six assists in all competitions.
Arsenal are long-term admirers of the striker, but Ornstein claims that the Gunners have some reservations over purchasing him.
The Gunners want a striker who can make an immediate impact and are more focused on signing Alexander Isak or Viktor Gyokeres.
The news is a huge boost for United and Chelsea, who are aiming to pursue a young striker with enormous potential over the summer.
Both clubs have been linked with Ipswich Town's Liam Delap, who has a relegation release clause worth £30m in his contract.
However, the Premier League duo are also monitoring Sesko's situation and could make offers for the highly-rated marksman.
Sesko could be purchased for around £62m in the next transfer window.