Davies was brought back for a second spell at The City Ground in February and has since overseen a run of six consecutive wins with Forest moving into play-off contention.
Al-Hawasi, who saw Alex McLeish leave by mutual consent last month after just 40 days in charge, is pleased with the changes that Davies has brought about at the club.
He said: "I'm really happy with Billy. The players are the same but maybe Billy has the magic wand.
"Billy will be with us like (Sir Alex) Ferguson is with Manchester United. If I was a dictator I would not bring Billy into my club because he doesn't like people to interfere, he is a strong manager. He is doing his job and I am doing my job. We are doing the right things together.
"It was difficult when it started. There was no consistency so we changed to another manager and another until we got the right one."
Forest now sit just eight points off the automatic promotion spots having taken 19 points from Davies' seven games in charge and Al-Hawasi clearly has eyes for the Premier League.
"We want to win as much as we can, not only to get into the play-offs, but to go directly to the Premier League."