Lukoil confirmed the leader's death on Thursday, but said Maganov passed away after a serious illness.
Meanwhile, two sources told Reuters that he fell from the sixth floor of the hospital and died from his injuries.
They also confirm reports from several Russian media that write that the circumstances surrounding his case are unclear.
Investigating authorities say they have analyzed the scene to determine how he actually died.
Two sources who knew Maganov well told Reuters that it is unlikely that Maganov committed suicide.
Demanded an end to the war
Lukoil is Russia's largest private company, and in a statement the company thanked the Maganovs for that achievement.
Shortly after the invasion of Ukraine, Lukoil's board called for an end to the conflict and also expressed its sympathy for the victims of "this tragedy".
Even so, Britain imposed sanctions on the company's billionaire president Vagit Alekperov, who then resigned in April.
Ravil Maganov had worked for Lukoil since 1993, overseeing the refining process, production and exploration.
He took over as chairman in 2020.
The fifth unexplained death so far
A number of senior executives connected to Russia's energy industry have died suddenly under unclear circumstances in recent months:
The day after Russia invaded Ukraine in February, Gazprom chief Alexander Tyulakov was found dead in his garage near St. Petersburg, according to Russian media.
In April, the millionaire and former head of Russia's largest liquefied natural gas producer Novatek, Sergei Protosenya, was found dead next to his wife and daughter in a residence in Spain.
Catalan police investigating the case have said they believe Protosenya killed his family before taking his own life.
In May, Russian media reported that a former Lukoil top, Alexander Subbotin, was found dead in the basement of a residence in Moscow.
In the same month, the former vice president of Gazprombank, Vladislav Avayev, was also found dead, also next to his wife and daughter.