Putin spoke of the proposal at a closed doors meeting with top ambassadors in Moscow on Thursday, the agency reported, citing people who were present at the gathering.
The US president reportedly asked Putin not to mention the idea at their joint press conference after the meeting to give him time to ponder the proposal.
Following the report, National Security Council (NSC) spokesman Garrett Marquis said that the White House did not consider supporting a referendum in eastern Ukraine.
"The administration is not considering supporting a referendum in the eastern Ukraine," Marquis said. "The Minsk Agreements are the process for resolving the conflict in the Donbas, and these agreements do not include any option for referendum. Furthermore, to organize a so-called referendum in a part of Ukraine which is not under government control would have no legitimacy."
Putin held a first face-to-face meeting with Trump in the Finnish capital of Helsinki. The two parties have discussed the current state of bilateral relations along with pressing issues on the international agenda.