Hodgson's current deal expires at the end of this season, but Mohamed Al Fayed is keen for the manager to commit his future to the Cottagers.
"It wasn't a difficult discussion," Hodgson told British broadsheet The Guardian. "We are basically in agreement and I've got to say it was very easy to come to that agreement.
"It seems that everyone is keen for me to stay and I've always made it perfectly clear that I'm happy to stay. I've never made any secret of the fact that I'm happy at Fulham and I'm enjoying the job here.
"It is just a matter now of putting the contract discussions that we have already had onto paper."
This Is London expect the deal to be worth £5 million and run until 2012.
The Englishman could then manage a Great Britain football team at the Olympic Games in London.
Alan Dawson, Goal.com UK
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