Riise was famed for spectacular strikes in his seven seasons with the Reds but has drawn a blank since returning to English football from a three-year spell at Roma last summer.
There would be no better place for the left-back to end his drought than on his old stomping ground.
He told Fulham's official website: "I know the fans and some people are wanting me to score. Believe me, I do as well.
"I've been very close and sometimes you need a bit of luck for them to go in.
"Because, it's not like I'm shooting from five yards. I have to shoot from 30 yards and things have to happen.
"Maybe it can happen at Anfield."
Riise, 31, admitted to feeling butterflies about playing again in front of the Kop.
"It was one of the first games I was looking for because I always wanted to come back," he said.
"Now, I'm going to be playing against them and it's emotional.
"I'm feeling a little bit - not nervous - but it's tickling a little more than usual, so I'm looking forward to it."
Fulham have never won at Anfield but they will arguably never have a better chance, with Liverpool enduring a miserable season at home in the Barclays Premier League.
Riise said: "We always play some good football away from home as well but we haven't got the results we maybe need or deserve.
"So, we're going into the Liverpool game really confident and hopefully we can play good football and get something out of the game.
"But it's a tough place to go to.
"They want to improve on their league position as well, so it won't be easy."