Peterson is to become a free agent after the 2014 season, meaning that he is now eligible to negotiate a fresh, long-term deal, or the franchise could risk losing him for nothing.
According to NFL Media reporter Ian Rapoport, the Falcons are looking to restructure Larry Fitzgerald's expensive contract, which will allow them some salary cap room and the ability to raise Peterson's $2.9m (£1.8m) wage.
Speaking to ProFootballTalk, Peterson said: "Me and my agent Joel Segal haven't talked about some of those contract possibilities yet. But hopefully we can get something done.
"We'll have to wait and see what happens regarding any restructure to my deal."
Peterson is regarded as one of the best in his position in the game, and since being drafted by the Cardinals in 2011, he has been selected for the Pro Bowl in each of his first three NFL seasons.