"We've been making excellent progress," Obama told reporters on Friday.
"We are quite close to an agreement. And I'm confident that it will be completed in a timely fashion."
Medvedev said a few "details" still needed to be discussed for a new deal to be reached, though he did not elaborate.
"Our positions are very close and almost all the issues that we've been discussing for the last month are almost closed," he said.
"A few technical details have remained which nevertheless need to be finalised in such an important agreement and I hope that we will do this in quite a short time."
Though the treaty has expired, both countries have agreed to continue to honour its main provisions, until the completion and legal ratification of a successor treaty.
The broad aim of the new treaty is to reduce the number of deployed warheads below the 1,700-2,200 allowed under Start.