Kompany has made the call after a poor start to the season, with Davies to take control.
The former Manchester City coach explained: "Look, we are looking forward to it. To the players who fit best in our system and philosophy, but also to the right framework next to it.
"We all only get to know each other fully and find our way in this new situation. That is how we came to this decision. The team needs stability, let that be clear. However, Vinnie loves the club so much that he always wants to give everything for Anderlecht. Every day. But now on competition days he will only concentrate on his match.
"This should allow us to work more efficiently and more result-oriented. The club can only reap the benefits of that clearer hierarchy."