Ex-England manager Hodgson has no intention of walking away prematurely and, should the club propose an alternative, would advise his replacement to stick to the initial agreement.
"If the club want to do that, I would understand it," said Hodgson after their home 5-1 thrashing by Leicester. "I wouldn't kick up any fuss about it, not at all.
"But if I was the new manager, I wouldn't take it at this moment in time.
"I think the new manager now would be in his rights to say, 'look, this season has not been the season it should be, I've got a job on my hands from pre-season, let the others that have been there for the last four to five months continue and I'll come in and do my stuff'.
"But if the club think it would be advantageous to bring the new guy in now then I will more than happily step aside and give him the chance to go to Chelsea next week - I've been to Chelsea lots of times.
"I don't believe in walking away. I wouldn't be upset or complaining, if that's what the club would like to do. It wouldn't hurt me particularly; I would understand it because I'm sure they would explain it in the right way.
"If that's what they want me to do, then that's what will happen but it's not going to come from me."
Edwards - who guided Forest Green to the League Two title this term - was unveiled ahead of kick-off.
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