Putin "feels absolutely comfortable in all formats that are comfortable for his interlocutors", Peskov said, adding that the Kremlin "doesn't rule out" a private meeting between the two presidents.
Trump, who is set to leave for Europe on Tuesday, will hold meetings with North Atlantic Treaty Organisation allies in Brussels, visit Britain, and then meet Putin in Helsinki for a one-on-one meeting on July 16.
The Kremlin said Putin did not plan to meet US lawmakers who are visiting Russian Federation this week.
It was the first time that Trump said that he would discuss the question with his Russian counterpart, even though he has insisted that there were no links.
The American-Russian summit 16 July is expected to touch on these United States efforts and how Russia could help in persuading the Palestinian Authority to reengage the diplomatic efforts of the United States government.
Moscow and Washington announced the summit date after Trump's National Security Advisor John Bolton met with Putin in Moscow last week.
President Putin had admitted the USA and Russian relations were in bad shape and that his meeting with Bolton increased hopes for restoration.
US-Russian relations have plummeted in recent years amid Russia's involvement in the Ukraine crisis and allegations that Russia meddled in the 2016 US presidential election. "We will have to wait and see".
Peskov said that President Putin "and Russian Federation are open for dialogue and jointly searching for compromises", TASS reported. Unlike many other news organizations, we have not put up a paywall.
Netanyahu and Putin meet periodically and discuss regional issues, particularly concerning mutual interests in the civil war in Syria and to avoid accidental clashes between Israeli and Russian forces that both operate in Syria.