Riise: Liverpool fans wanted me back
The Norwegian joined the Cottagers from AS Roma earlier this month, where he will team up with brother Bjørn Helge Riise.
But the 30-year-old has said fans of the Reds, for whom he played 339 times between 2001 and 2008, had told him he should return to Merseyside.
"I've heard people say [Liverpool] haven't really replaced me, but that is not my concern," Riise said in The Sun.
"If they wanted me back they could have made an effort. I know a few of the fans wanted me back.
"I achieved a lot when I was at Liverpool and this is my type of football.
"I needed a new challenge after that and improved as a player but it was always in my mind to come back."
During his time at Liverpool, Riise became a cult hero among fans for scoring a spectacular long-range free-kick against rivals Manchester United. He went on to win the League Cup, FA Cup and Champions League with the Anfield side.
Riise is set to make his Fulham debut in the Londoners' Europa League qualifying match against Crusaders on Thursday evening.