The Reds are in the market for a new boss after relieving Billy Davies of his duties on Monday in the wake of a humbling 5-0 defeat to arch-rivals Derby County.
Neil Warnock emerged as an early frontrunner for the post, but the former Sheffield United and Crystal Palace boss has turned down the chance to take charge at the City Ground.
Ex-West Ham United and Watford boss Zola and one-time England manager Hoddle are now considered to be among the favourites to inherit the Reds' reins.
Al Hasawi admits the pair are in his thoughts, with tentative talks having already been held with their respective representatives.
He said after Forest's 1-0 defeat to Charlton Athletic on Tuesday night: "Both are very good managers, we will have to see them. We will see their plans for the remaining games."
Al Hasawi has also refuted suggestions that Warnock ended talks with Forest amid fears that he would not be granted the level of control he demands in running a football club.
The Kuwaiti businessman added: "Previous managers know me very well, I never interfered in their job.
"I never told them what to do or what to play. Sometimes I shared things together with them, that doesn't mean you are interfering.
"If you say an opinion, does that mean I am interfering? It's not, it's only my opinion.
"If I say 'Why we don't play this player or that player', it's just opinion. In the end, it's his call. He's fine with it, but I never interfere or blame the manager for not doing this or that. Never.
"Otherwise, why should I bring in a manager, I will be the manager!
"I am director of football for seven years, I used to be a player in Kuwait, I understand football. Maybe I should save the club £1million and be the manager.
"With all respect for Neil Warnock, I never interfere with the manager's decision. The manager will say 'yes' or 'no', not Fawaz."