An odd and difficult-to-confirm story that keeps popping back onto news cycles, almost zombie-like, describes an alleged attempt by Saudi Arabia to bribe Russia into dumping its Syrian client, Bashar al-Assad, with a huge $15 billion arms deal and lucrative oil-and-gas concessions.

The news reports, though many of them are dated today, actually refer to a four-hour July 31 meeting between Russian President Vladimir Putin and the head of Saudi intelligence, Prince Bandar bin Sultan, at Mr. Putin's Novo Ogaryovo dacha outside of Moscow.

The meeting was widely reported by Arab media within days, along with the version, apparently leaked by the Saudi side, that Prince Bandar had offered Putin generous Saudi contracts to buy Russian tanks, attack helicopters, and other weaponry in return for Russia's agreement to scale down its support for Mr. Assad and not to veto any more UN Security Council resolutions pertaining to Syria.

That story was flatly contradicted by the Kremlin on Aug. 9. Putin's foreign policy architect, Yury Ushakov, admitted that the meeting with the Saudi intelligence chief had taken place, but insisted that only "philosophical" matters had come up.

"No specific military collaboration issues were discussed," although a mutual concern was expressed regarding the Syrian civil war, the official RIA-Novosti agency quoted Mr. Ushakov as saying. "It was a very intense and interesting conversation of a philosophical nature."

Russia and Saudi Arabia have plenty of issues to talk about, in principle, and some sources suggest that secret meetings like this have been going on regularly for quite a few years.

The two countries are the world's No. 1 and No. 2 oil producers – they alternate in first place from year to year – yet Russia does not cooperate with the Saudi-led Organization of Petroleum Exporting Countries (OPEC), a cartel that seeks to maintain balance between global oil supply and demand in order to keep prices buoyant.

One report of the Bandar-Putin meeting quotes the Saudi official as offering not to "contest" Russia's gas market in Europe and other forms of cooperation that could prove profitable for Russia.

"Let us examine how to put together a unified Russian-Saudi strategy on the subject of oil. The aim is to agree on the price of oil and production quantities that keep the price stable in global oil markets," one media report quotes Bandar as telling Putin.

Besides a common – if often clashing – interest in Middle Eastern affairs, Russia accuses Saudi Arabia of exporting a militant brand of "Wahabbi" Islam that Moscow claims is fueling extremist activity in its mainly Muslim regions of the north Caucasus and the Volga republic of Tatarstan.

Some versions of the story about Bandar's meeting with Putin suggest that the Saudi intelligence chief went so far as to offer Russia its help in containing potential terrorist threats to the upcoming Sochi Winter Olympics, and suggesting that the Games could be in danger if Moscow fails to come to an agreement about Syria.

Some Russian experts say the accounts of what Bandar proposed to Putin may be accurate, but say they doubt Putin – who is able to splash out over $50 billion of Russia's own oil money to host the Olympic Games – would renege on his own strongly expressed and oft-repeated policies on Syria in exchange for a few billion dollars in dubious arms contracts.

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"Yes, it seems Saudi Arabia made a proposal to buy $15 billion worth of Russian arms, but the Kremlin made clear that it wasn't making any behind-the-scenes deals. And that was the end of it," says Vladimir Sotnikov, a Middle East expert with the official Institute of Oriental Studies in Moscow.

"It was probably some kind of trial balloon. But Saudi Arabia is no friend of Russia's, and it really wouldn't suit Putin to do deals behind Assad's back. Russia is standing on principles of international law regarding Syria, and it has enough points in favor of its position that it sees no reason to risk all its credibility with some move like that. Even if it were an offer to join an oil price-fixing cartel, even then Russia wouldn't go along. No bargain like that is going to happen," says Mr. Sotnikov.