"We are not ready yet to talk about concrete dates," Peskov said.
On June 21, Trump said that he was "looking at the possibility" of a meeting with the Russian president in July.
Despite denying of having any information about the possible meeting, the Kremlin spokesman has confirmed that US National Security Adviser John Bolton is scheduled to visit Russia.
"As far as we know, indeed, such a trip will take place. This is all we can say," Peskov told reporters.
Earlier, Donald Trump hinted at a get-together with President Putin in an interview with Fox News and later suggested this summer as a possible date.
On June 10, Vladimir Putin said his meeting with the US President would take place as soon as Washington is ready for it.