The Sun says Burke is set to join Hull after failing to agree personal terms with Derby.
Rams boss Frank Lampard tried to hijack Burke's £1.5million Tigers move last night.
Burke, 21, was tempted by Lampard's Hammers connections but talks have broken down.
It leaves Hull with a clear path to land the highly-rated centre-back.
Burke left West Ham's pre-season training camp in Switzerland to fly home for a medical.
He is reluctantly quitting West Ham after being told his appearances would be limited under new boss Manuel Pellegrini.