According to a source close to the company, ConocoPhillips has decided to leave the country entirely and would most likely seek arbitration to resolve the dispute.
Four other companies – America's Chevron, Norway's Statoil, Britain's BP and France's Total – have reportedly agreed to the partial takeover.
They plan to sign an accord that will keep them in the massive Orinoco oil reserve projects, a government official said.
An official announcement on the final outcome is expected on Tuesday, the deadline set by Chavez for the companies to either accept his terms of continuing operations with a minority stake or to leave the country.
On May 1, the government seized control of the operations of the Orinoco projects, which were among the last privately run fields in the South American nation.
Chavez gave the six companies extra time to work out a deal over the projects' new ownership structure.
Sticking points include asset valuation, compensation for lost value, and decision-making rules in the future joint ventures, according to industry officials.
Companies that agree to stay on in the four projects have two months before a final deal is submitted to the Venezuelan congress for approval.
Those that reject the deal can leave and take Venezuela to court or accept a government offer to negotiate compensation for several months for the nationalised Orinoco assets, several sources familiar with the talks said.
Chavez's high profile showdown with oil companies and his broader nationalisation drive covering the telecommunications and electricity sectors apparently have the support of Venezuela's poor majority who got him re-elected in December.
The president has used of billions of dollars in oil revenues to finance social programmes.