Yesterday the UN was refusing to permit the plane into Iraqi airspace, but Mr Zhirinovsky was insisting he would go ahead, possibly today. As publicity stunts go, it looks promising. It should allow both the Russians and the Iraqis to demonstrate what caring people they are, and what a rotten idea it would be to try to bomb Saddam Hussein into opening up his secret palaces to UN weapons inspectors.
But it would also be another reminder that, when it comes to Iraq, Russians can get to the parts that others cannot reach. The Kremlin's current cosiness with the Iraqis, reflected in its efforts to resolve the current crisis diplomatically and Boris Yeltsin's theatrical warnings of a third world war, has deep roots in the Soviet era.
Anxious to consolidate its influence in the Middle East, and to counterbalance that of the US (particularly in Israel), the Soviet Union signed a friendship treaty with Baghdad in the early 1970s, which led to a multitude of arms and technology deals, often conducted on Soviet credit.
Some $10m (pounds 6.25m) of these debts remain unpaid - a sum which Moscow, with its huge short-term debts and collapsed economy, now sorely needs. This, and the prospect of benefiting from lucrative oil contracts, is why the Kremlin has been keen to see UN sanctions lifted.
The Soviet-era relationship was complex and sometimes tense, particularly following the outbreak of the Iran-Iraq war in 1980, a conflict which Leonid Brezhnev described as "absolutely senseless". Officially, the USSR took a neutral position, maintaining ties with Iraq while trying not to alienate the newly-arrived, usefully anti-Western, ayatollahs in Tehran.
By the time Saddam Hussein invaded Kuwait in 1990, there were thousands of Soviet citizens in Iraq working as military advisers and technical specialists. As Mikhail Gorbachev was to admit, the invasion put the Soviet Union in an awkward position, not least because of its multi-million dollar interests there. Russia's current Foreign Minister, Yevgeny Primakov, an Arabic-speaking KGB veteran and long-term acquaintance of Saddam, took an active role in the last-minute diplomacy which tried to avert violence. Ultimately, though, the Soviets supported the use of force - marking the first instance of US-Soviet co-operation in the Middle East.
Moscow was never much at ease with the war, which was seen domestically as a betrayal of an ally, and pressed hard for an early conclusion. Mikhail Gorbachev later wrote in his memoirs that "Washington preferred the argument that a political settlement would be a mistake for the United States, since this would have raised the Soviet Union's prestige, something that many of the President's advisers always perceived as not in America's interests."
It is a reflection of the cooler relations that now exist between Moscow and Washington - and also, perhaps, of the price of Nato expansion - that Boris Yeltsin's Russia appears more stridently opposed to bombing the Iraqi dictator into line today than Mikhail Gorbachev's broadly supportive, crumbling empire.