Walcott, who played with the Gunners head coach, says that he knew the Spaniard would be a top manager.
Arteta joined Arsenal in 2011 from Everton, spending five years at the Emirates Stadium before retiring.
"The turning point for me in terms of how I viewed Mikel Arteta was an experience I had with him as a player at Arsenal," Walcott told William Hill's podcast, Up Front with Simon Jordan.
"It was at a time when we weren't making the top four.
"We had training in 30 minutes and he locked all the players in the dressing room, as if he was the manager. He was taking control of the whole space and telling us how it is. In that moment it was like he was the manager, and that was the turning point for me.
"That's when I thought he could go on to be a manager. Arsene Wenger was waiting for us to come outside for training but we weren't coming out because Mikel stopped the training session. He was such a strong character that even Arsene was afraid of him."