But what Russia has never contemplated is UN troops in its own backyard. “Summoning the UN deep into Russia’s historical space is a serious step”, Dmitri Trenin, head of the Moscow Carnegie Centre, told The Economist recently.

There does seem to be a shift in Moscow’s thinking on this highly sensitive issue.

Last month President Vladimir Putin put forward a plan for the deployment of UN troops in south-eastern Ukraine. Not that he imagines their use along the Russian-Ukrainian border – that would be too much – but he wants them to divide the fighting forces inside Ukraine.

An objection is that this would formalise the internal division in Ukraine. But even so, it is a bold move as it would mean UN soldiers getting in the way of the secessionist, Russian-orientated, militia in south-eastern Ukraine. They wouldn’t be able to expand the territory they already control without overrunning UN troops.

The idea of a UN peacekeeping operation in Donbas, eastern Ukraine, was first discussed over three years ago by a small group of independent Russian and American experts on the Finnish island of Boisto.

Their proposals were rejected by both the Ukrainian government and Moscow. But now there is a sea change. Both Putin and the Ukrainian president, Petro Poroshenko, seem to favour a UN intervention although they see how a deployment could be made somewhat differently.

The fighting which used to be fierce is subdued at the moment. However, the cease-fire negotiated at Minsk by Russia, France, Germany and Ukraine in February 2015 is regularly violated and some of the heavy weapons that were pulled back from the demarcation line have returned.

The Minsk II agreement appears to have lost momentum.

Moscow justifiably blames Kiev for not implementing the agreement. Critical promises have not been followed through, such as changing the country’s constitution, passing a law to establish the special status of the Donetsk and Lugansk enclaves in Donbas, holding local elections, underlining their Russian-language rights and declaring an amnesty.

A divided Poroshenko government, partly under the influence of right-wing movements whose pedigree stretches back to Nazi times, seems incapable of moving on these vital issues. It doesn’t help that Ukrainian public opinion feels like it is being pushed to compromise because of the Russian threat.

Mistakenly, some believe that if the chips are down US and Nato forces will come to their aid. This is doubtful, to say the least, although voices in the US Congress such as Senator John McCain have been pushing for arms to be sent.

Putin still seems to think he can go on hoodwinking the world about Russian supplies of heavy weaponry to the dissident forces. He maintains that the “soldiers are men following the call of their hearts to fulfil their duty or are voluntary taking part in hostilities, including in south-east Ukraine”.

Russia appears to believe that without these local militias the Poroshenko government would just walk in.

Despite Western sanctions, there has been little shift in the Kremlin line. Indeed it has gone on the offensive with large-sized war games and some quasi-confrontational sabre-rattling by its air force above the Baltic Sea.

Both in Washington and Moscow, some macho policymakers have talked about the necessity of preparations for a limited nuclear war (although, in all probability, there never could be a limited one).

This is why some of us think Putin’s recent talk on a UN role is a big step forward.

Fyodor Lukyanov, who edits the influential Global Affairs, and who has the ear of the Russian Foreign Ministry, argues that Putin should expand his UN ideas. According to Alexei Arbatov, head of Russia’s Centre for International Security, a UN force must be strong enough to ensure a 100% cease-fire and the withdrawal of heavy weapons.

The mission would look less like the failure in Kosovo in 1999 and more like the success in Cyprus that began in 1974, separating the Greek-speaking half of the island from the Turkish-speaking.

UN forces have been deployed along the dividing line for 43 years and are still there. They have held back what many Greeks have long believed is the danger of a renewed threat of ethnic cleansing of the kind that the Turks tried to carry out in 1974. At first the UN troops had to fight their way in.

In the Ukraine case, peace between the two sides in Donbas would not be just a dividing line between pro-Russian and pro-Ukrainian forces it would probably in time bring peace on the Russian-Ukraine border.

Putin’s idea must be explored.