Arizona's Board of Regents must approve the extension during its meeting June 5-6.
Graham has coached in Tempe for two seasons with a record of 18-9. He led the Sun Devils to a bowl victory his first season and took them to the Pac-12 championship game last season.
Graham also will have numerous performance and academic incentives, including a bonus of 50 percent of his salary for winning a national championship and a cumulative grade-point average of 3.0 or a graduation rate of 95 percent for his team.
He received a one-year contract extension through 2018 in September that will pay him gradual raises.