Owner Massimo Cellino says Cook is considering improved terms after a highly impressive first season as a professional at Elland Road, according to the YEP.
Cook’s emergence from Leeds’ academy was one of the highlights of a hard and underwhelming Championship term but the midfielder’s existing contract expires next summer, leaving United exposed to interest in him.
The teenager has become one of Leeds’ most valuable assets in the space of a year, catching the eye with his performances in midfield.
Cook, who was part of England’s European Under-17 Championship-winning squad last summer, made 38 appearances this season before an ankle ligament injury ended his campaign early.
He was named as the Football League’s apprentice of the year last month.
Aston Villa and Newcastle United have both been credited with interest in him in the lead-up to the summer transfer window.