Free trade negotiations between New Zealand, Russia and its customs union partners, Belarus and Kazakhstan began under the presidency of Dmitry Medvedev.
Nine rounds of negotiations have been held but the last one was in July last year.
Mr Key did not rule out raising with Mr Putin the issue of two New Zealanders having been charged under Russian law with piracy after taking part in a Greenpeace protest against a drilling platform in the Arctic sea.
However he said Foreign Minister Murray McCully had already raised the issue with Russian authorities.
Mr Key helped to mark Mr Putin's 61st birthday yesterday by joining with other Apec leaders to sing him 'Happy Birthday' when he arrived at the leaders' retreat. Apec's Indonesian hosts also presented him with a birthday cake.
The birthday wishes occurred in a waiting room outside the retreat venue. As the leaders filed into the venue, Mr Putin approached Mr Key and shook his hand.
The meeting of 12 countries negotiating the Trans Pacific Partnership will take place this evening, NZ time, with Mr Key substituting for US President Barack Obama as chair.
Mr Key, Trade Minister Tim Groser and senior officials met last night with United States Trade Representative Mike Froman about the meeting and Mr Key was expecting to talk to Secretary of State John Kerry this morning.
Leaders attended a gala dinner last night and will have a group photograph on the beach this afternoon.
Indonesia President Susilo Bambang Yudhoyono has asked representatives of four Pacific countries, Fiji, Kiribati, Marshall Islands and Solomon Islands to attend an informal session with the leaders.
Fiji will be represented by Foreign Minister Ratu Inoke Kubuabola.