Lyondell uses the Houston refinery to produce feedstocks for its chemical plants. The refinery can run a variety of cheaper high-sulfur crude oils. In the past few years it has been running a large amount of Canadian oil.
The 263,776 barrel per day (bpd) Houston refinery was restoring production on Monday after an early Thursday morning power outage, the latest in a string of fires, shutdowns and power outages that have cut the plant's production throughout year.
Saudi Aramco-Motiva emerged as the leading contender over the weekend, when Lyondell's management evaluated proposals from potential buyers, the sources said.
Aramco-Motiva and Canada's Suncor Energy were exchanging proposals with Lyondell in the past few days, according to the sources.
Little was heard about another potential buyer, Valero Energy, the sources said.
Saudi Aramco, Motiva, Suncor and Valero did not reply to messages seeking comment.
The refinery has been valued at about $1.5 billion based on an average price between $5,000 and $6,000 per barrel of refining capacity in recent sales of U.S. refineries.
The Lyondell refinery is well known to Saudi Aramco's partner in Motiva, Royal Dutch Shell.
Lyondell's refinery supplies dry gas to Shell's joint-venture refinery seven miles (11.25 km) east in Deer Park, Texas. Aramco and Shell announced plans in March to divide Motiva's three refineries, distribution terminals and retail networks between them. Aramco is to keep the Motiva name.
It was unclear if the Lyondell refinery will remain with the post-breakup Motiva once the split takes place on April 1, 2017.
Negotiations on the final distribution of assets after the breakup were continuing as of last week, according to Motiva.