The former Liverpool left back is due to undergo a medical at Fulham, suggesting the Cottagers have agreed terms with the Serie A club.
"He's coming for a medical. If that's okay we've got ourselves a very good player," Fulham manager Martin Jol told the club's official website.
Riise won the Champions League and the FA Cup during seven years at Anfield and his younger brother, Bjorn Helge, is already on the books at Craven Cottage.
Fulham were held to a frustrating goalless draw by Faroe Island minnows NSI Runavik on Thursday night but still progressed to the second qualifying round of the Europa League.
Jol's men failed to capitalise on a flurry of first half chances against the Faroe Island part-timers.
But Fulham advanced 3-0 on aggregate and they will meet the Crusaders from Northern Ireland next Thursday.
"It's not easy playing here but I feel if you create six or seven chances in the first half you should score," Jol added. "In the first half we had seven or eight good chances and we have to be more productive and eager to score. In the second half I think we only had two chances which weren't enough.
"We have to get fitter and more creative and come up with solutions. In this sort of game you need players that can make a difference and we didn't have that.
"Defensively we were sound and we didn't concede, which is important but they did have one chance at the end. Technically you can see the difference between the players but they did well."