The companies said in July they were in talks for Delek to buy a 20 percent stake in EnQuest's Kraken oilfield, in a deal that could have been worth $162 million (122.17 million pounds).
The companies had been unable to reach an agreement, EnQuest said on Thursday, but did not provide details.
(Reporting by Mamidipudi Soumithri in Bengaluru; Editing by Sunil Nair)