The 19-year-old's future has been the subject of much speculation in recent weeks, with Manchester United believed to be keen to bring him to Old Trafford.
Chelsea have also been credited with an interest in the Slovenia international, who has scored 13 goals in 42 appearances since breaking into the Salzburg first team.
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.
Man United are thought to have recently met with the youngster's agent, Elvis Basanovic, and Salzburg to discuss a possible deal during this summer's transfer window.
However, Austrian reporter Marko Stankovic has claimed that Sesko wants to remain at Salzburg for another season before switching clubs ahead of the 2023-24 campaign.
"According to our information, Sesko wants to stay in Salzburg for another year so that he can make the leap like an Erling Braut Haaland," Stanovic told Sky Sports Austria.
"That's Sesko's plan. Next year at the latest we will talk to him about a really good transfer."
According to Italian journalist Fabrizio Romano, Leipzig have now come to an agreement with Salzburg and Sesko over a transfer in the summer of 2023.
The report claims that the Bundesliga outfit could complete the deal this week in what would be a huge blow to Man United, who had seemingly earmarked the centre-forward as a possible acquisition in the final weeks of the summer window.
Anthony Martial's hamstring problem, coupled with Cristiano Ronaldo's lack of fitness, saw Christian Eriksen start as a false nine in Man United's Premier League opener with Brighton & Hove Albion on Sunday.
A difficult contest saw Erik ten Hag's side suffer a 2-1 defeat, and the club are said to be determined to bring in a new centre-forward before the transfer window closes.
Bologna's Marko Arnautovic is the latest player to be linked with a switch to Old Trafford, with the Red Devils already thought to have had a bid rejected for the 33-year-old.
The 20-time English champions will be bidding to bounce back from the disappointing loss to Brighton when they continue their league season away to Brentford on Saturday.
However, it is unclear whether Martial will have overcome his injury in time for the contest, which could open the door for Ronaldo to start despite the ongoing speculation surrounding his future.