Kelly has been out since breaking a foot during a 38-24 win at Colorado on Sept. 13.
"This is Taylor's football team," Graham said. "He's earned that."
The Sun Devils (5-1, 3-1 Pac-12) have gone 2-1 during that stretch with Mike Bercovici at the helm. In three starts, Bercovici has completed 63 percent of his throws for 1,243 yards with nine touchdowns and two interceptions.
He had a five-touchdown performance -- which included a last-second, game-winning Hail Mary -- on the road at No. 16 USC. And he threw one touchdown and no interceptions in a 26-10 win last week over No. 23 Stanford.
"I'm not a head coach that's going to change quarterbacks up very often, especially one I've won 22 games with," Graham said. "If he's ready to go, which I think he will be, he'll go. That doesn't mean Mike won't play. We're not the same team we were before Taylor got hurt. I think we're better because of how Mike has developed."
In the first three games, Kelly had thrown six touchdown passes with no interceptions and rushed for two scores.