Adams has previously questioned whether the armband was too heavy for the Gunners midfielder.
But Odegaard has forced a rethink, as Adams told talkSPORT: "I just said, 'Maybe it should be Declan (Rice),' and I said this about Harry Kane for the England team as well.
"When you've got a forward, sometimes you need to mix it up, you need to change things - put a faster player on or a bigger player for crosses or someone that can create things.
"And he's (Odegaard) part of that process and he's a Dennis Bergkamp (type of player), he's a talented, talented player.
"But he's not going to be on the pitch 24/7, so I just went for Gabriel (Magalhaes) or Declan Rice (to replace Odegaard as captain), that was my argument.
"He wasn't positive (with the ball last campaign), but he has been this season, he really does put the ball in now.
"It was like he was hesitating and hesitating and he was slowing play up, but this season, I've seen a significant change in him."
On Odegaard as a leader, Adams also said: "I heard within the camp - (and) I'm not in the camp - I hear he's very good Odegaard, and the lads love him.
"So I can understand why they're united behind him and that's absolutely fine.
"And he comes off (when substituted) and he throws the armband to Gabriel at times, most of the time he does to (Bukayo) Saka and throws it to Saka, and then he (Odegaard) gives it back to Gabriel when Saka doesn't play.
"So I think they've got many leaders they've got many captains, they've got a fantastic squad of players that are going to win the league this year.
"It's as simple as that so I don't read anything into it."