The Slovenia international is also wanted by Manchester United, but now favours joining Newcastle, reports Delo.
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The Slovenian outlet states Arsenal were also interested in Sesko before going cold after their swoop for Sporting CP striker Viktor Gyokeres.
Despite the push of United, Sesko wants to move to the Magpies.
However, any deal could hinge on the future of Alexander Isak, with Newcastle rejecting a £110m offer from Liverpool for the Swede this week.