The quarterback has one season remaining on the deal he signed with the NFC South side when he was drafted in 2008.
The team's general manager told NFL AM: "For Matt right now, he's not worried about it because he knows that something is around the corner, as we do.
"I can't put an exact date on it. This is a long-winded way of saying I'm hoping we can agree to something going into the season."
The Falcons have made the playoffs in four of the five years since signing Ryan.