Key also wants to talk to Obama and Medvedev about the Security Council's role in Syria peace efforts and about Helen Clark's bid to become UN Secretary General.
New Zealand is chairing the Security Council this month and Key will be chairing the council at a special Syria discussion on September 21, to which leaders have been invited.
Key has had a long -standing relationship with Medvedev.
Obama may have a little more time on his hands in Laos because he has cancelled a meeting with new Philippines president Rodrigo Duerte after Duerte said he would call him a "son of a whore" if he raised the issue of killings of drug dealers.
(He has also called Pope Francis a "son of a whore" for causing a traffic jam in the Philippines.
Key is also planning a dinner with Australian Prime Minister Malcolm Turnbull at the EAS.
Key today laughed off the fact that after a meeting with British Prime Minister Theresa May at the G20 in China, Turnbull tweeted that no two countries were closer than Australia and Britain - something that Turnbull has said about New Zealand as well.
"I don't think we should feel too precious about it."
The EAS leaders are expected to disucss tensions in the South China Sea but with China among its number, it is not likely to issue a tough statement on it.
The East Asia Summit (EAS) is a meeting of the 10 leaders Asean countries as well as the United States, China, Russia, India, South Korea, Australia, New Zealand.
Eight of the EAS members are among the 12 countries that negotiated the Trans Pacific Partnership and leaders are expected to have a meeting on the sidelines with Obama about the prospects of ratification.
After the East Asia Summit, Key will head to the Federated States of Micronesia for the Pacific Islands Forum.
