Adams insists the armband should be taken from Odegaard for the new season.
"He's got a really big call to make this year and for me he hasn't done it," Adams said. "The call is to make Declan Rice the captain.
"I think Declan is my kind of captain, and it might free Odegaard up to play with a bit more freedom.
"Every now and again as a manager, you have to put someone who reflects you, who reflects the football club that you think can actually take you to the next level.
"And I'm seeing Declan Rice as a captain but I'm saying to Arteta: "Come on, step up now. It's your time to be a winning manager and a fantastic manager, because you're not going to win the league with Odegaard as captain."
