Having coming through the youth ranks at Aalesund, the 33-year-old played for Monaco, Liverpool and Roma before joining the Whites in 2011.
Riise was initially a first-team regular under Martin Jol, but has fallen out of favour and only appeared twice in the English Premier League for Fulham this term.
A January move to join up with his brother Bjorn Helge at Lillestrom has been mooted and, with his contract up at the end of the season, the full-back concedes he could soon leave Craven Cottage.
"I have lived abroad for almost half my life," Riise told TV2. "The time may be ripe to move home in the new year. It would be fun to end my career in Lillestrom with my brother, but I have not taken any decision on what to do yet. I feel at least I can play in four or five years."