GAZ is part of the Basic Element group that holds the assets of Russian businessman Oleg Deripaska and already has a partnership with Volkswagen.
It was not immediately clear how big a stake VW was talking about taking, or the value of the potential deal and a decision on size has yet to be made, one of the sources said.
Both GAZ and Basic Element declined to comment, while a spokesman said VW does not comment on market speculation.
“There are talks, they are trying to reach an agreement. Deripaska has long been looking for a partner and VW does not have a Russian partner,” one car industry source said.
A source close to VW also confirmed that talks were in progress, but said the possibility of the carmaker taking a stake in GAZ is not the only matter under consideration.
The stake deal, if it goes ahead, would show that major Western companies are forging ahead with investments in Russia despite political tensions over Ukraine and allegations, denied by Moscow, of Russian meddling in foreign elections.
Other global automakers have already taken stakes in major Russian vehicle manufacturers. Russia’s biggest carmaker, Avtovaz (AVAZ.MM) is controlled by the Renault-Nissan (7201.T)(RENA.PA) alliance, while Russian truck maker Kamaz is part-owned by Daimler (DAIGn.DE).
Sollers, a Russian firm which manufactures light commercial vans, has no global automaker as a shareholder, though it has a joint venture with Ford (F.N)
Russian car sales, which shrank from 2015 as the economy slowed sharply, have recovered this year and new car sales rose 17.3 percent year-on-year in October to 148,597 units, the Association of European Businesses (AEB) lobby group said this month. It was the eighth consecutive month of sales growth.
VW is already a major investor in Russia, having sunk 1.75 billion Euros (1.5 billion pounds) into its operations. It has a vehicle plant and an engine plant in Kaluga, 150 km south of Moscow.
Under its existing partnership with GAZ, the Russian firm assembles VW brand and Skoda cars, while VW supplies 2.0 litre diesel engines for light commercial vehicles made by GAZ.
Addional reporting by Katya Golubkova, Polina Devitt and Jack Stubbs in Moscow and Andreas Cremer in Berlin; Editing by David Goodman and Alexander Smith