The list does not include current acting Central Bank chief Tatyana Paramonova, said the source, who asked not to be named. But it was not clear whether Paramonova had been completely ruled out as a candidate.
Yeltsin is due to nominate one candidate to the Duma over the next week or so.
The source said the list currently under consideration includes former Finance Minister Sergei Dubinin, currently working with Gazprom; Yeltsin's chief economic adviser Alexander Livshits; and Promstroibank President Yakov Dubenetsky.
Before working with Gazprom, which was once headed by Prime Minister Viktor Chernomyrdin, Dubinin was deputy chairman of Bank Imperial.
"Dubenetsky seems the most preferable," the source said.
He said Yeltsin had not yet sent his nomination to the Duma, and as far as he knew had not yet decided it.
The Duma failed to muster enough votes in July to confirm Paramonova as chairman, after rejecting her a first time in April. Under Russian law, Yeltsin can nominate her one more time.
Paramonova has been praised by economists for stabilizing the Russian economy this year through tight monetary policies which have brought inflation down to below 5 percent a month and steadied the ruble against the dollar.
But she was unpopular with many commercial bankers, who have a powerful lobby in the Duma, because the tight monetary policies curbed banks' easy trading profits.
Paramonova replaced Viktor Gerashchenko, who was sacked by Yeltsin after the ruble's "Black Tuesday" crash against the dollar one year ago.
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