The Republic of Ireland international is undergoing a medical and manager Roy Hodgson is hoping a deal to sign the former Chelsea and Blackburn Rovers forward will be completed in the coming days.
"I think he's been allowed to come down and he's having a medical," Hodgson said on Saturday evening.
"If all goes well I'm hoping the details will be finalised both on his personal contract and the details between ourselves and Newcastle.
"I'm hoping that will be finalised at the beginning of next week and, all being well, I'll be able to tell you he's a Fulham player next week.
"Until it's completed, it's better to be prudent, but I'm very hopeful we'll have Damien with us.
"Last year we were extremely fortunate as we had so few injuries. I'm expecting this year to have to be without players occasionally and that's why we need the quality of people like Damien Duff to put into the team."