"The man fell out of the sixth-floor window and died as a result of his injuries," a source told TASS.
Lukoil confirmed the death of its chairman on Thursday in a statement published on its website.
Ravil Maganov "passed away following a severe illness", Lukoil said, making no mention of a fall.
"Maganov immensely contributed to the development of not only the company, but of the entire Russian oil and gas sector," the company said.
Lukoil, Russia's second biggest oil and gas company, made headlines in March when it called "for the soonest termination of the armed conflict" in Ukraine.
"We express our sincere empathy for all victims, who are affected by this tragedy," the company's board of directors said in a statement to shareholders, staff and customers at the time.
"We strongly support a lasting ceasefire and a settlement of problems through serious negotiations and diplomacy."
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The firm produces more than 2 per cent of the world's crude oil and employs more than 100,000 people.
RIA Novosti quoted a law enforcement source Thursday as saying Maganov "most likely committed suicide".
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"Investigating authorities are working on the spot to establish the causes of the incident," the source told RIA.
At least five prominent Russian businessmen have reportedly died by suicide since late January, according to previous CNN reporting