Arteta is the frontrunner for the job after talks with club officials at his mansion in Manchester on Sunday.
De Bruyne said: “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. If he doesn't, it's his decision, but why, otherwise, start coaching in that way?
“Whatever he wants to do, you have to do it. If you want to grow, you need to take opportunities when they come."