According to press secretary of the Russian president, there are many topics for discussions between Putin and Trump, TASS reported.
Peskov indicated that thus it is in the common interests "both president could find opportunities for a rather long communication."
The press secretary pointed to many recent positive events in the Syrian settlement. However, he continued, bringing the settlement to a new level requires cooperation.
On North Korea, Peskov was cited by RIA Novosti as saying that there is no co-operation between Russia and the US on the North Korea issue for the time being.
"There is no co-operation so far. Only periodic exchanges of views," he said.
Russian President Vladimir Putin and US President Donald Trump may meet at the APEC summit in Vietnam next week.
Peskov was commenting as Trump prepares for a five-country visit of Asia, where leaders have been rattled by his rhetoric about North Korean leader Kim Jong-un.