The Kremlin said in a statement that the two close trade and energy partners were holding "substantive discussions" on building up the capacity of Hungary's Paks facility.
The statement said Paks was responsible for producing 40 per cent of the energy consumed in the former Warsaw Pact state.
It added that Russia supplied about 80 per cent of Hungary's oil and 75 per cent of its natural gas.
"The negotiations with Hungary have reached their active stage," Russia's Rosatom state atomic energy corporation chief Sergei Kiriyenko told the Interfax news agency.
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Paks is run by Hungary's state-run MVW -- a group that also imports natural gas from Gazprom and would like to negotiate a price cut with the Russian energy giant.
The Hungarian parliament in 2009 approved a decision to add two more reactors to the four already operating at Paks.
France's Areva and US electric company Westinhouse along with Japanese and South Korean power suppliers had previously expressed interest in bidding for a contract of the Hungarian plant's expansion.
Any deal with Russia could lead to domestic criticism of Orban because no formal bidding process for the plant's expansion has yet been launched.