The 21-year-old is widely regarded as one of the brightest young forwards in Europe and was heavily linked with a big-money exit from Leipzig in the summer.
However, Sesko decided to commit his future to the Bundesliga club in June when he signed a new long-term contract until 2029.
The Slovenia international has spent just over a year at Leipzig and has scored 22 goals in 49 appearances across all competitions, netting six times in eight games at the start of this season.
Sesko was a standout performer for Leipzig on Wednesday night when he scored a brace in a 3-2 home defeat to Juventus in the Champions League.
TBR Football claims that around 20 clubs, including Arsenal, had scouts present at the Red Bull Arena, but interested suitors may find if challenging to prise Sesko away from Germany in the near future.
In-demand Sesko to remain at Leipzig long term?
Speaking about his future to Italian news outlet La Gazzetta dello Sport prior to kickoff, Sesko said: "I don't comment on transfer rumours. I'm happy in Leipzig and that's why I recently extended my contract.
"I want to achieve even more great things here, Leipzig wants to grow a lot and I want to accompany the team on this very intriguing journey."
Arsenal allegedly explored the possibility of signing Sesko in the summer, with Mikel Arteta known to be in the market for a new centre-forward to provide competition for Gabriel Jesus and Kai Havertz.
However, the Gunners eventually decided against adding a new number nine to the senior ranks, and while they are still thought to hold an interest in Sesko, they currently have no plan in place to table a fresh offer for the £55m-rated striker.
Man United, meanwhile, are said to still have a long-term interest in Sesko and could rival fellow interested suitors from across Europe, including Serie A giants AC Milan, for his signature.
The Red Devils bolstered their attack in the summer with the addition of Joshua Zirkzee, but he has recently been linked with a January move to Juventus, who could propose a swap deal involving Dusan Vlahovic, who has also been linked with Arsenal.