Have they actually made a bid? Can they?
Manchester United made their first formal offer for Sesko on Tuesday.
BBC Sport chief football news reporter Simon Stone reports it is an initial fee of £65.2m, rising to £73.8m.
They had been thought to want to be sure Sesko wanted to join them before making their move.
Old Trafford sources say they do not have to sell players before making more signings – but do accept finance will have to be generated by several players unwanted by Ruben Amorim.
Why would Sesko want to join them?
Sesko would be a likely starter at one of the world’s biggest clubs if he joined Manchester United.
Rasmus Hojlund, also aged 22, has only scored 14 Premier League goals in two seasons since his £64m move from Atalanta.
By contrast Sesko has scored 27 Bundesliga goals in that time, having joined Leipzig from Salzburg in the same summer.
“Although many external United observers feel any spare income would be better spent on a physical, energetic central midfielder, Ruben Amorim spent most of last season moaning about his side’s inability to score often enough,” said Stone.
“Clearly he feels an upgrade is required on Rasmus Hojlund at the top of the pitch. To that end, United are willing to listen to offers for Hojlund, which may end up being part of their negotiations with RB Leipzig.”
And he could be part of an all-new front line with Matheus Cunha, a summer signing from Wolves, and ex-Brentford man Mbeumo joining for about £130m in total this summer.
He could get plenty of service from the three players nearest him if he was the focal point up top.
Bruno Fernandes created more chances than any other Premier League player last season – 91 – with his team-mates scoring 10 of them.
Mbeumo was fifth on the list, creating 70 chances for Brentford team-mates, and Cunha was 15th, with 57 opportunities laid on for Wolves players.
Why might Sesko not want to join them?
There are some fairly obvious reasons why Sesko might decide Old Trafford would not be the best destination to keep his career on this upward trajectory.
For one, they are not in any European competition this season. Sesko has played in the Champions League in three of the past four seasons, and the Europa League in the other.
And he would be joining a team who finished 15th last season, their worst campaign since they were relegated in 1973-74.
Boss Amorim has been given the opportunity to rebuild this summer, having only taken over midway through last season – but a bad start could see a managerial change too.
And Sesko would have to buck a fairly dramatic trend. There is a very strong argument that Portugal midfielder Fernandes is the only outright success United have had in the transfer market since 2016.
