The Magpies had offered €80 million for Sesko, but Manchester United made a higher bid of €75 million plus €10 million in bonuses on Tuesday.
Sesko is now reportedly favouring a move to Old Trafford, and Newcastle is not willing to wait for him. Instead, they plan to quickly identify and pursue other targets.
The club is considering Aston Villa striker Ollie Watkins and RB Leipzig's Lois Openda, who plays alongside Sesko. They also remain interested in Brentford's Yoane Wissa, despite the club's rejection of a £25 million bid last week.