It's a thought that Moscow might be weighing, amid the turmoil and revolution in Ukraine that led to the ouster of President Viktor Yanukovych from Kyiv.
The prospect of Russia surrendering its influence on its smaller and less economically stable neighbour raises questions about how Putin will respond to the crisis over the border, according to analysts specializing in eastern European politics.
"The thinking is, if Putin loses Ukraine, what can he hold onto at this point?" said Jeff Sahadeo, director of the Institute of European, Russian and Eurasian Studies at Carleton University.
"Then the next step is people either say, ‘If Yanukovych can be [ousted], then maybe Putin can be as well,' or, ‘If Ukraine can split away from the Russian orbit, maybe we can, too.'"
Meanwhile, Sahadeo said, Putin will be facing calls from pro-Russian populations in eastern Ukraine to intervene in some way.
"The question is how do you do it?" he said.
Russian leaders in the Kremlin are likely debating a course of action, but haven’t decided how to proceed. That’s been clear based on Putin’s conspicuous silence on the matter, experts say.
Shutting off gas supplies
There are certain levers at Putin’s disposal, namely Russia's control of natural gas and energy supplies, which Ukraine and Europe are reliant upon. Kyiv already owes a hefty gas debt to Russian firms.
But shutting access to Ukraine would also hurt Russia’s economy.
"It would be shooting itself in the foot, because two-thirds of Russian gas exports to Europe go through Ukraine," said Taras Kuzio, a research associate with the Canadian Institute for Ukrainian Studies.
As for the possibility of Russian military intervention, Kuzio said such a thought would be "fanciful" owing to the risks involved.
Sahadeo agreed that sending in Russian troops would almost amount to war.
A wait-and-see diplomatic approach could be a wiser move.
Yanukovych is in hiding, accused of mass murder in the killings of anti-government protesters, and Russia appears to be losing its grip in a tug-of-war against the European Union for Ukraine.
"At the moment, really, Russia is in a state of shock," said Andrew Wood, a former British ambassador to Moscow from 1995 to 2000, and currently an associate fellow at the independent London-based think-tank Chatham House.
"Russia has to decide whether it will retreat into basic grievance, or adjust to the fact that Ukraine … is not a state which is simply passive for the Russians and the West to contend over."
Tymoshenko, the devil you know
Ukraine’s parliament has set May 25 as the date for early presidential elections to find a successor to replace Yanukovych.
Putin could hope for a democratically elected candidate to come into power by that time who would be more sympathetic to Russian interests. Governor of the pro-Russian Kharkov region, Mikhail Dobkin, who announced his intention to run, could be one such choice, Sahadeo said.
Another possibility would be former prime minister Yulia Tymoshenko, released from prison over the weekend following corruption allegations linked with a Russian gas deal.
However, Tymoshenko’s time may have passed, and Ukrainians may still perceive her as a corrupt figure who also may have health issues.
"I don’t think she’s burned all her bridges with Putin, but she’s a naturally fiery and combative person," Sahadeo said.
"Putin would have to swallow his pride and say, "At least it’s the devil I know."
As for Yanukovych, who was last seen in the Russian-friendly Crimea, he will probably be on his own at this point, said Kuzio, with the Canadian Institute for Ukrainian Studies.
Ukraine 'the biggest prize'
Even Yanukovych’s own Party of Regions has turned its back on him.
"The Kremlin views him as somebody who wasn’t tough enough, who could have killed more people to suppress what they see as a fascist coup d’état supported by the West," Kuzio said.
That doesn’t necessarily mean Russian authorities would go so far as to apprehend Yanukovych.
It would be easy for him to find protection in the Crimea, where a Russia's Black Sea naval fleet is based.
One way or another, the stakes are high for Russia, Sahadeo said. The West has already exerted influence over swaths of eastern Europe, with the Baltic states having already joined NATO and the EU, and Moldova and Georgia having signed EU state agreements.
But Ukraine represents "the biggest prize," sharing an emotional connection with Russia as "the heartland of Kyivan Rus'," Sahadeo said, referring to the medieval east Slavic state.
While the Kremlin fretted about a potential terrorist attack during the Sochi Winter Olympics undermining Putin’s image, Sahadeo said, the reality is the loss of Ukraine would do far more damage.
"He can blame outside elements all he wants, but rhetoric won’t do anything in this cause, because it’s clear that’s consensus in parliament and in Kyiv that Ukraine can be taken into a different direction," he said.