Talks between Paris and Moscow have been mired by disputes for months, with the Kremlin throwing open the contract to an international tender last month.
Still, recent statements made by senior Russian military officials Moscow have confirmed that France and Russia are in exclusive talks for the purchase of Mistral-class ships.
In a recent meeting with his French counterpart, Russian Foreign Minister Sergey Lavrov said negotiations were "proceeding intensively" and "include a number of technology transfers."
In separate remarks, Defense Minister Anatoly Serdyukov told Moscow's ITAR-Tass news agency that the Kremlin was "expecting the detailed financial conditions" from France to push the deal to its final stages.
"We will examine them and then refer to experts, not just in Russia but also abroad," he added.
Serdyukov accompanied Lavrov during the Paris talks with French President Nicolas Sarkozy.
Designed to attack the shore from the sea, the Mistral class is viewed as an ideal weapon for Russia against possible uprising by nearby countries.
Details of the deal remain sketchy, but Russian officials have suggested that the price tag for each vessel was estimated at around $380 million. French officials have also indicated that the building of the ships would be a "50-50 project."
The Mistral amphibious assault ship can carry 16 heavy or 35 light helicopters, dozens of tanks and more than 900 soldiers.
The deal has drawn concern from NATO allies apprehensive the transfer of Western naval technology to their former Cold War foe. Still, if clinched -- along with rights to construct several other vessels of the same class in Russia -- the deal would mark the most important transfer of military equipment to Russia by a NATO member country.
Moscow's announcement last month to hold an international tender follows heated complaints raised by Russian shipbuilders claiming that it would be illegal for Moscow to seal the deal with France without a previous tender.
Defense News reported that other competitors considered for the carriers include Russia's Zvezvda shipbuilder in the Far East which has a joint venture with South Korea's Daewoo Marine Shipbuilding and Engineering.
With its cutting edge technology, the Mistral is prided as the most powerful asset of the French fleet.
Russia owns only one Soviet-built aircraft carrier, which is much smaller than its U.S. counterparts and is considered outdated.
In all, Russia has expressed interest in buying four Mistral ships with the prospect also of eventually building such vessels on Russian soil.