The Norwegian put pen to paper on a three-year deal at Fulham last week for an undisclosed fee. However, the left-back revealed that Liverpool fans were keen for him to return to Anfield.
"I've heard people say they haven't really replaced me and that is not my concern," ESPN quotes Riise as saying. "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."
Despite considering a return to his former club, the 30-year-old has assured Fulham fans that he is looking forward to competing in the Premier League at Craven Cottage.
Riise will potentially be playing alongside his brother Bjorn, who joined the Cottagers in 2009.