The deputy head of Russia's cultural protection agency said a British government order to protect the paintings from seizure had helped to defuse the row over the safety of the art collection.
"We are completely confident that our cultural treasures will be protected from third parties in Britain," Rosokhrankultura chief Anatoly Vilkov told the Echo of Moscow radio station.
He added that "if the museums solve all of the technical questions" the artworks will be sent directly to London from Dusseldorf, Germany, where they are currently on display.
However, one of the four museums involved in the exhibition said Monday that a final agreement had not yet been secured.
Russian authorities had feared that the paintings in the "From Russia" show at London's Royal Academy could be seized by people claiming they were looted from their families during the 1917 revolution or by companies holding major Russian government debts.
The 120 works from Russia's top four museums include works by Impressionists Paul Gauguin, Henri Matisse and Vincent Van Gogh.
"We are no longer against bringing the paintings to Britain," said Irina Antonova, the director of Moscow's Pushkin Museum, one of the four involved in the exhibit, the Interfax news agency reported.
"But everything is not clear yet," she said. "As far as I understand a final announcement on the question of the exhibition will be made on January 9" by Russia's ministry of culture.
Britain's new law "gives a fundamentally new and constructive background to complete negotiations on the exhibition," Interfax quoted Russian Foreign Ministry spokesman Mikhail Kamynin as saying on Monday.
The situation has provoked a diplomatic tussle between London and Moscow, whose relations have chilled after Russia's refusal to extradite the chief suspect in the death of ex-spy Alexander Litvinenko in London last year.
In another dimension to the dispute, Russia has said it will close down two branches of the British Council, which promotes British culture worldwide, in January over alleged tax irregularities.
Britain's ambassador to Russia on Saturday linked the two disputes, saying London was disappointed that its work to enable the exhibition had not been reciprocated.
"We have worked very hard to maintain our cultural relations precisely at the moment when it looks as if the Russian authorities may be tempted to undermine them," Anthony Brenton said in an interview with Interfax.
The exhibition of 120 paintings from the State Hermitage and Russian Museum in Saint Petersburg and the Tretyakov Gallery and Pushkin Museum in Moscow was due to open in London on January 26.
Insurance on the exhibit currently in Germany expires on January 6, Interfax reported.