The 19-year-old's future is currently the subject of much speculation, with a number of clubs said to be keen to sign the Slovenia international before the end of the transfer window.
Man United are believed to have recently met with Sesko's agent Elvis Basanovic and Salzburg to discuss a possible move for the teenager this month.
According to Sportklub, the 20-time English champions have now tabled a concrete offer for the striker, with the club desperate to win the race for his signature.
Sesko has started the 2022-23 campaign in impressive form for his Austrian club, scoring twice and providing one assist in three appearances in all competitions.
Meanwhile, he has now scored 13 goals and registered eight assists in 41 matches for Salzburg, having enjoyed a breakthrough 2021-22 season at the club.
Sesko still has another four years left to run on his contract at Salzburg, placing the Austrian champions in a strong position when it comes to his future.
A recent report claimed that the Red Bulls had placed a £45m valuation on the Slovenia international, although it is unclear whether Man United's offer meets the asking price.
Man United are looking to sign another attacker this summer amid the speculation surrounding Cristiano Ronaldo's future, with the club currently lacking options in the final third of the field.
Sesko, who is 6ft 4in, has previously been compared to Manchester City forward Erling Braut Haaland.
"Such comparisons motivate me and give me energy," Sesko told reporters. "They do not represent pressure. I will listen and learn so I can be even better than he is. My teammates at the club tell me that Haaland and I are very similar, especially in terms of speed. Most of them even tell me that I'm better than him!"
Sesko's agent Basanovic said that a number of "really big clubs" tried to sign the youngster back in 2019, but Salzburg ultimately won the race.
"We had a lot of offers from really big clubs," Basanovic told SPOX. "Had we decided on the money, Benjamin would have moved to England or Italy.
"But we decided to look at the bigger picture and the Salzburg project. The biggest clubs in Europe tried to get him. The interest in him was huge; I have never seen anything like it before."
Man United will begin their 2022-23 Premier League campaign with a home match against Brighton & Hove Albion on Sunday afternoon. body check tags ::