Liverpool are on the brink of making an official approach for the Fulham boss. But Al Fayed said: "I don't think he'll leave me. I'm sure he'll have lots of approaches from other clubs, but I give him anything he wants to reach results and we have a very good relationship."
Despite increasing speculation that Hodgson is Liverpool's No.1 target, no official approach has yet been made.
A senior Fulham source told the Sunday Mirror: "Roy's his own man and if an approach was forthcoming I'm sure he will sit down and evaluate the situation. He is very private and keeps his own counsel, so you can never second guess what he's going to do.
"However, the indications are it would take something extraordinary to convince him to leave Fulham and I'm not sure given all the documented financial problems at Liverpool he'd see that as ideal move.
"Roy has an incredibly good relationship with the owner as well. Given that he is pressing ahead with player recruitment for the new season, I'm not sure that is an indication he is planning to leave."