Murphy Oil Corp.'s (MUR) refinery on the U.K.'s Pembrokeshire coast faces closure as its U.S. owner's search for a buyer has run into trouble, The Sunday Times reports.

The newspaper said Murphy Chief Executive David Wood wants a resolution soon over the Milford Haven site, which has been up for sale for two years.

Wood said, "In the absence of an acceptable offer we are evaluating the potential conversion of the facility into a storage terminal."