Last week, on Exxon's behalf, several courts ordered a freeze on $12 billion of Petroleos de Venezuela SA's foreign assets due to a dispute over oil fields Venezuela nationalized in 2007.
The Venezuelan oil exporter, known as PDVSA, said it would stop all business with Exxon except for work at a jointly owned Chalmette, La., refinery, The Wall Street Journal reported Wednesday.
Venezuela will probably sell its crude to a third party, who would then sell it to Exxon, an industry analyst said. Venezuelan oil is difficult to refine and Exxon has the capacity to refine it.
Exxon can also turn to Canada or Mexico to supply heavy oil.
"There are very limited markets where that crude can go and there's a very high [Venezuelan] dependence on the petrodollars," Ruchik Kadakia of Cambridge Energy Research Associates told the Journal.
ConocoPhillips also abandoned its Venezuelan oil fields when Venezuelan President Hugo Chavez nationalized the fields but is negotiating with the government rather than take its complaint to court.
Exxon, on Tuesday, offered to keep negotiations with PDVSA open, the report said.