"We will discuss whether it is possible for Russia and NATO to cooperate better, because the era of the Cold War is definitely over," she said in her weekly video message.
During the two-day summit, the three leaders will also discuss increased cooperation between the European Union and Russia, Merkel said.
"The Russian president has proposed a common security architecture. He is working step-by-step to define this architecture -- of course in a spirit of partnership of all European countries with Russia," she said.
The three leaders will meet in the French Channel resort of Deauville on Monday, aiming to bind Moscow more closely into a partnership with the West.
NATO will unveil its new security concept next month at its summit in Lisbon, and Western leaders hope Medvedev will confirm in Deauville that he will attend the meeting and and give his support to their vision.
Meanwhile, Merkel welcomed Germany's selection as one of five new non-permanent members of the UN's Security Council.
"This will allow us to assume more international responsibilities over the next two years," she said.
