Kostin, the head of Russian state bank VTB and an ally of President Vladimir Putin, "had a conversation with Mr Schwab and he is aware of this decision," the bank said in a statement to AFP on Tuesday, referring to Klaus Schwab, founder of the World Economic Forum whose annual meeting in Davos, Switzerland, is attended by global political and business leaders.
The decision was made under pressure from Washington, the FT said, citing sources familiar with the situation.
Spokespersons for Deripaska and Vekselberg did not issue an immediate comment.
State news agency RIA Novosti quoted a source close to Deripaska as saying that the aluminium magnate had no plans to travel to Davos in January because he was no longer heavily involved in running his businesses.
"So his participation in the forum would have no sense," the source was quoted as saying.
The trio are believed to be close to Putin and attended the forum in the past.
Deripaska was particularly famous for throwing wild parties in Davos, with vodka, caviar and dancing Cossacks on offer.
Putin has not attended the forum for a decade, sending top government officials instead.
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