"For the meeting to take place, Putin must meet with Zelensky," the source said.
It is unclear, however, whether a bilateral meeting between Putin and Zelensky is intended or whether Trump is requesting trilateral talks.
The New York Times reported on the possible meeting between Putin and Trump the day before.
According to the newspaper's sources, the US president expressed his intentions in a telephone conversation with European leaders on August 6.
The New York Times publication mentions Trump's meeting first with Putin, and then Trump's meeting with Putin and Zelensky.
Moscow later announced that Russia and the United States had reached an"agreement in principle" on a meeting between Putin and Trump.
"A proposal was received from the Americans, which seems quite acceptable to us," said Yuri Ushakov, an aide to the Russian dictator.
However, the New York Post notes that"in speaking to the press, Trump expressed caution about the prospects of the meeting," explaining that he has already experienced disappointment due to Moscow's empty promises of peace.
"He talks beautifully and then bombs everyone," the US president said of the Russian dictator.
Meanwhile, the Russian dictator once again announced on Thursday that the"conditions" for meeting with Zelensky had not been met.