"Almost everything has been done," Putin told the Ria Novosti news service. "But when I say 'almost' I mean some things still need to be polished."
Among the facilities requiring more attention is the 40,000-seat Fisht Olympic Stadium, which will be the site for the opening and closing ceremonies.
"Some of the equipment should be installed and additional preparation work should be finished," Putin said.
The president also talked about a flexible pricing policy, with tickets for events such as bobsled starting as low as $15.
"It's important to provide the possibility for people from various Russian regions to attend this festival of sport," he said.