The Gunners have spoke with City assistant Arteta about replacing Unai Emery as their manager.
And De Bruyne thinks his club shouldn't stand in the way of the Spaniard.
"He came here three years ago, and had to find his way a little bit, because to transition from player to coach is a little bit different," De Bruyne said to the Manchester Evening News.
"He is finding his role really, really good right now. I guess one day he will want to be a head coach – I don't know when but he's helping the team in the way he thinks he can help and is doing a good job.
"He is helping us a lot, but if he gets a good opportunity to be a head coach, and he thinks it's time for him to take that, I think as a club you need to let somebody go.
"You want to grow as a head coach, I guess. If he doesn't, it's his decision, but why, otherwise, start coaching in that way?
"It's difficult for me to explain. Whatever he wants to do, you have to do it – if you want to grow you need to take opportunities when they come."