Megson made the offer in the wake of Saturday's 2-0 defeat at Barnsley but has been told that the Forest board still have faith in him despite a poor start to the season.
"We are where we are and everyone has got to roll their sleeves up and do what is expected of them, myself included," said the manager.
"I have had a message of support from the chairman and spoken to the chief executive (Mark Arthur) and I like working for this football club.
"But the methods I employed at West Brom to get results don't appear to have the same effect here. I am going to have to adjust my thinking."