"I'm excited about seeing what he does this week," Gannon said.
Dobbs was asked after the game Sunday if he expects to remain the starter and said: "A hundred percent."
Gannon, in his first season as the Cardinals' head coach, had declined to name a starting quarterback against the Commanders until right before the game, citing "competitive advantage."
QB Kyler Murray is on the physically unable to perform list after injuring an ACL in Week 14 last season. He will miss at least the first four games.
ESPN's Josh Weinfuss contributed to this report.