Hodgson, as then manager of Italian club Udinese, proved to be a great help to Moyes when he was taking his UEFA Pro Licence several years ago.
Fulham are in dire straits in 19th in the Barclays Premier League, effectively seven points from safety because of their inferior goal difference but Moyes has issues of his own as he pushes Liverpool for the fourth Champions League place.
"Roy helped me when I was doing my pro licence four or five years ago when he was manager at Udinese," explained Moyes.
"You have to do a foreign visit as part of it and I was over there with Roy and him and his wife looked after me really well.
"Udinese did as well and so I know Roy quite well.
"I wish him success and I hope he does well at Fulham but not until after my game that is for sure."