News agencies Bloomberg and Reuters on March 23 quoted Kremlin sources as saying that Chubais, who was responsible for relations with international organizations, had left the country.
Russia's state news agency TASS quoted a source as saying that Chubais had left his position but did not confirm whether he was still in Russia or not.
No reason was given for Chubais's departure. He is the highest-profile official on Putin's team to resign since Russia launched its attack against Ukraine on February 24.
The 66-year-old Chubais was first deputy prime minister, finance minister, and chief of the presidential office when Boris Yeltsin was Russia's first president following the collapse of the Soviet Union.
Chubais was a key reformer and an ideologue of the privatization program in Russia in the early 1990s.
Since the start of the war, many Western countries have implemented crippling sanctions on Russia and those close to Putin.
Information from Reuters was used in this report