"They say June, there are even specific [preliminary] dates", Ushakov said in an interview with Russia's Rossiya 1 broadcaster, without elaborating further.
When asked if a working discussion about the summit is underway, the official answered in the negative.
"So far no, but a signal has been received, and we will consider it. Of course, we will make a decision taking into account many factors", Ushakov stated.
The aide also talked about how Putin's participation in the US-organised climate summit should be viewed.
"[It should be viewed] as our great interest in climate issues being solved. They can only be solved together, that is why we definitely participate in such events, in all of them", the aide explained.
At the same time, Russian Foreign Minister Sergei Lavrov noted that the US president's proposal to hold a summit with his Russian counterpart was a positive sign. However, he stressed that Moscow was still ready to take measures if Washington further escalated tensions in bilateral relations.
Tensions between the two nations have been escalating over the past few months as the US has repeatedly accused Russia of meddling in the 2020 presidential election, which Moscow has denied on multiple occasions. Washington also introduced sanctions against several Russian companies and individuals.
Ties further worsened after Biden agreed with a journalist calling Putin a "killer" in a March interview with ABC, and threatened the Russian president will have to "pay a price" for the alleged meddling in the 2020 vote.