The talks proposed by France will only take place if Russia does not invade its neighbour, the White House said.
The meeting 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 proposal 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.
The second exchange happened in the early hours of Monday Moscow time, and followed a 15-minute conversation Mr Macron had with Mr Biden.
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.
In a statement that confirmed the proposal, the White House also said Russia appeared to be "continuing preparations for a full-scale assault on Ukraine very soon", and that the US was ready to impose "swift and severe consequences" should it happen.
The Biden administration estimates Russia has amassed up to 190,000 troops around Ukraine, including separatist forces in the Donetsk and Luhansk regions in eastern Ukraine.
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.
Mr Putin agreed on the need to "prioritise a diplomatic solution" to the crisis, according to the French presidency. It said "intense work" would be carried out to enable a meeting "in the next few hours" aiming for a ceasefire.
The Kremlin said Mr Putin blamed 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.
However, the French presidency said both leaders 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.
UK Prime Minister Boris Johnson said Mr Putin's commitments to Mr Macron were a "welcome sign" he might still "engage in finding a diplomatic solution". But Mr Johnson called on Mr Putin to "step back from his current threats and withdraw troops from Ukraine's border".
Photo EPA Caption: Russian and Belarusian soldiers have been training together