Sesko was linked with Arsenal, Manchester United and Newcastle during the summer market.
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And Mintzlaff admitted to Kicker: "Sesko had offers from the Premier League that were worth over 70 million euros.
"It was important to us that we were able to put together a top team after the big upheaval last year and continue to work based on a certain continuity."
Sesko, 21, penned a new deal to 2029 in June. In 49 games for the Saxons so far, Sesko has scored 22 goals.