The Croatian revealed he had had discussions with technical director Luke Dowling and chief executive Xu Ke two days after his team drew 1-1 at Brighton on Monday.
Centre back Hegazi, who was earning about £60,000 per week, signed an initial loan deal with a £3million obligation to buy.
"I said what I want to say and it needed to be said," said Bilic. "I also said it after the game when we came back to the training ground the day after to the people from the board, from the club, and for me that's finished.
"I had to protect the team and the staff and everybody, my position. It's nothing secret but now I want to close the chapter."
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!