The 32-year-old has spent two seasons in west London, making 75 appearances, having returned to the Premier League from Roma following a lengthy spell at Liverpool.
He still has a year remaining on his contract but the Cottagers will allow him to leave without a fee.
Bundesliga side Werder Bremen are believed to be interested, although a number of other overseas clubs have also made enquiries about the former Norway international.
"Yes, it looks like I will be parting company with Fulham this summer," Riise told Press Association Sport.
"Fortunately there is an agreement for there to be no transfer fee, so let's see what the rest of the transfer window brings."
Riise has started two of Fulham's five pre-season friendlies, with Martin Jol rotating him with Kieran Richardson.