Russian prosecutors were preparing official extradition documents on Tuesday for Vladmir Gusinsky when the US and Israel stepped in, said a Greek diplomat.
"There have been contacts on a diplomatic level between Greek, US and Israeli officials in which the latter expressed their view that Gusinsky should not be extradited," the diplomat told AFP.
A spokesman for the US embassy to Greece said he did not want to comment on possible US involvement in the case.
"The Israeli consular section offers Mr Gusinsky exactly the same services it would offer to any other Israeli citizen under similar circumstances," an Israeli embassy spokesman said.
However, the spokesman did not confirm this meant Israel had offered the 50-year-old Gusinsky assistance not to be extradited to Greece.
"There have been contacts on a diplomatic level between Greek, US and Israeli officials in which the latter expressed their view that Gusinsky should not be extradited."
He was detained at Athens international airport last week after arriving from Tel Aviv. On Monday, Gusinsky was remanded in custody by a Greek prosecutor who has sent the case to a court which will consider the extradition request.
Greek media reported that powerful political operators in the US had intervened on his behalf with both Washington and the Greek authorities.
In Moscow, Interfax said prosecutors had received an official notification from Greece of Gusinsky's detention.
"Today this notification has been translated into Russian and we have begun to prepare documents requesting Gusinsky's extradition to Russia," an official in the prosecutor's office said.
The tycoon fled Moscow three years ago after being sought by prosecutors for allegedly swindling state-dominated gas giant Gazprom out of 250 million dollars (230 million euros).
He is also accused of fraudulent privatisation and money laundering.
Gusinsky successfully fought off extradition when he was twice briefly detained in Spain after fleeing Russia in 2000, the year Putin came to power. Gusinsky then moved to Israel.