Newcastle have had a club record bid for the 22-year-old accepted by RB Leipzig, but Manchester United submitted their own offer on Tuesday.
And while that bid has not yet been accepted by the Bundesliga club, all parties are now aware that it's a move to Old Trafford that Sesko wants this summer.
If, as is now expected, Manchester United come to an agreement with Leipzig and Sesko gets his wish, Newcastle will have to stomach missing out on yet another leading target this summer, the latest in a lengthy list.
James Trafford, Bryan Mbeumo, Liam Delap, Joao Pedro, Hugo Ekitike were all wanted at St James' Park but have all moved elsewhere, leaving the Magpies' squad looking extremely thin with just 10 days to go until the start of the Premier League campaign.
As things stand, Anthony Elanga and Aaron Ramsdale are the only signings at Newcastle this summer in what was hoped would be a transformative window where the Magpies significantly bolstered their squad in preparation for their Champions League return.
Not only have they been dealt a string of transfer setbacks, they're also currently dealing with the Alexander Isak situation, with the Swedish striker having made known his desire to leave the club for Liverpool.
But as things stand, Newcastle won't entertain the prospect of allowing their star striker to leave unless they have a replacement in place. They do have other striker targets who they will now turn to but time is not on Newcastle's side. They remain hopeful of striking a deal for Brentford's Yoane Wissa and are also interested in Aston Villa's Ollie Watkins.
Liverpool remain interested in Isak but are aware of Newcastle's stance and aren't expected to return with an improved offer until Newcastle source a replacement.
But what's not clear at this stage is what will come out of Eddie Howe's showdown talks with Isak this week, with the striker having returned to the club's Benton base on Monday after missing the pre-season trip to Asia and instead flying to Spain where he trained alone at former club Real Socieded.
Newcastle remain without a sporting director after the exit of Paul Mitchell early this summer.