Fayed launched an attack on Hodgson after the former Fulham boss left Craven Cottage for Liverpool in 2010, saying that he hoped that he'd take the Reds "downhill".
Furthermore, he called Hodgson a "bugger" and claimed that replacement Mark Hughes was "better looking".
"I've been called worse than a bugger," Hodgson said. "I suppose he was right on the Liverpool thing.
"There is no animosity from me. I am not expecting to see him but I would shake his hand."
Hodgson arrived at the Hawthorns earlier this year, after spending less than one season at Liverpool.