Fulham insist they have had no approach yet but are braced for a fight to hang on to their manager.
Owner Mohamed Al Fayed recently made £1.5BILLION from the sale of posh London store Harrods and has vowed to use it to plough more cash into the club.
Hodgson is also a candidate to eventually replace England boss Fabio Capello and could miss out if he joins Liverpool this summer and the Italian quits after the World Cup.
"And everyone thinks that's what he would love to do.
"He could miss out on that if he gets tempted by Liverpool and then the England job comes up not long after.
"There's also the question of Liverpool being up for sale at the moment. Roy could go there under the current owners, new men come in and the job could end up being very short-term."