Odegaard, 26, has missed 11 games for Arsenal so far this season due to numerous fitness issues, with his latest being a knee injury sustained in the 2-0 win over West Ham.
The Norway international is now back in training and could be set to return as Arsenal take on Bayern Munich at the Emirates.
Speaking ahead of the game, Arteta revealed a decision about Odegaard’s inclusion hasn’t been made just yet.
“We’re going to have a meeting now to decide on Martin,” Arteta told reporters on Tuesday. “He was very close for the previous game, so we are hopeful that tomorrow he can be in the squad as well.”
Arteta also revealed that Gabriel Jesus is close to returning from his ACL injury.
“(Jesus is) quite close to be fair, and it’s earlier than we expected,” Arteta said, before adding “... in the next few days he’s going to have another step to make, with a game that we’re going to organise for him, and after that he’s just going to be knocking on the door, because he’s Gabriel, a winner, that’s how it’s happened.”