The talks proposed by France will only take place if Russia does not invade its neighbour, the White House said.
The Kremlin, meanwhile, said there were no “concrete plans” for a summit.
It is hoped that such talks could offer a possible diplomatic solution to one of the worst security crises in Europe in decades.
US officials say intelligence suggests Russia is ready to launch a military operation, which Moscow denies.
The proposed summit was announced by the French presidency after two phone calls between President Emmanuel Macron and Mr Putin, which went on for almost three hours in total.
Mr Macron’s office said details of the possible summit would be discussed during a meeting between US Secretary of State Antony Blinken and Russian Foreign Minister Sergei Lavrov on Thursday.
Russia has massed more than 150,000 troops close to Ukraine’s borders, according to US estimates.
US company Maxar said new satellite imagery showed multiple new field deployments of armoured equipment and troops from Russian garrisons near the border with Ukraine, indicating increased military readiness.
The French presidency said both leaders had agreed to resume talks through the Normandy Format, a group created to resolve the conflict in eastern Ukraine that includes Russia, Ukraine, France and Germany.
However, the Kremlin later said it was “premature to talk about any specific plans for organising any kind of summit”.
“There is an understanding that dialogue should be continued at the level of foreign ministers,” spokesman Dmitry Peskov said. He added that a meeting was possible “if the heads of state consider it appropriate”.
The Kremlin says Mr Putin blames the Ukrainian military for the escalation of tensions. Ukraine has rejected this, saying Moscow is engaged in a provocation campaign aimed at creating a pretext for an intervention.
- ON THE GROUND: Criss-crossing Ukraine with President Zelensky
- CONTEXT: Satellite images show Russian activity near Ukraine
- BACKGROUND: Is Russia going to invade Ukraine?
Earlier, Russia announced the extension of military drills in Belarus, where 30,000 Russian troops are deployed, that were due to end on Sunday. A Belarusian statement blamed the “deterioration of the situation” in eastern Ukraine as one reason for extending the exercises.
Speaking on CNN, Secretary Blinken said “everything we are seeing suggests that this is dead serious” and that “we are on the brink of an invasion”.
His comments came as unverified reports in the US media suggested Washington believed an attack could be launched imminently.
CBS News reported the US had intelligence that Russian commanders on the ground had received orders to proceed with an invasion and were now making specific battle plans on how to attack.
The report said an invasion would begin with a cyber-assault followed by a campaign of missile and airstrikes, before ground units attempted to take the capital Kyiv.
And an unnamed intelligence official told CNN close to 75% of Russia’s conventional forces were now poised at the Ukrainian border. The concentration of Russian forces within striking distance of Ukraine was highly unusual, the source said.
But Ukraine’s Defence Minister Oleksii Reznikov said an attack “tomorrow or the day after tomorrow” was unlikely as no Russian “strike groups” had yet formed near the border.
In other developments:
- Rebels in Luhansk said two civilians were killed in a shelling attack by Ukrainian forces, but the authorities in Kyiv denied any involvement
- Thousands of civilians, out of a population of several million, are being evacuated from the separatist territories into Russia while men of fighting age are being mobilised to fight
- The US embassy in Moscow warned Americans of potential attacks in public places in Russia, including along the border with Ukraine. A Russian foreign ministry spokesperson criticised the move
Mr Putin has been demanding assurances that Nato will not admit Ukraine, a former Soviet state with close ties to Russia, while the Western alliance denies it poses any threat to Russia.
There are fears that a Russian military intervention could start a war even bloodier than the conflict in eastern Ukraine which has cost at least 14,000 lives.
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