Al Hasawi is happy to carry on in his current role until the end of the season, to avoid disrupting the club's promotion challenge.
He revealed he has spoken to several candidates about the position and hopes somebody will be appointed officially in June.
"I run the club on a day-to-day basis," said Al Hasawi, who has spent in the region of £30million since taking over the club 20 months ago.
"I speak to (manager) Billy (Davies) on a daily basis, even if I am not in Nottingham. If I am in Nottingham, I am always at the club. If there is a decision to be made, it will come to me.
"I am running the club right now, as chairman and chief executive. But it is too much. I would like to bring a chief executive to the club as soon as possible. But it has to be the right man. I do not want to bring somebody in who is not the right person.
"I want to bring somebody in who will have a good connection with everyone, with myself, the manager and the staff.
"At the end of the day, if they come in and succeed, I will succeed. I want somebody who will work with us. We are doing well. At the moment we will bring in the chief executive to start working with us in the summer.
"We have met with some people and, whoever it is, they will start on June 1.
"We have three or four people in mind for the job. But, if they take it, they will start at the beginning of June."