The 29-year-old has been a key member of Martin Jol's side this season, making 27 appearances in all competitions, and bagged his first goal for the club in Saturday's 2-2 draw at Sunderland.
The Cottagers have an option to buy the German at the end of the season and Riether has revealed his desire to stay in the Premier League.
"I’d like to remain here," he confirmed to the club's official website. "Fulham have an option to buy me and so I think in the next few weeks there will be talks about my future.
"At the moment I can’t really say what will happen. But I like it here and I’m thankful that Fulham gave me the chance to play in the Premier League."
Riether, who has become a fan favourite at Craven Cottage, puts his success down to hard work and says he considers himself a Fulham player and never gives too much thought to his 'on loan' status.
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"In my mind, I’ve never thought of myself as being here ‘on loan’, I give my best as if I’m here for a long time. I’ve never felt I was coming here for a short time, for a holiday. I always give everything in each game I play and see myself as a Fulham player, not a Koln player.
"I’ve never had this before at my previous clubs so for me it’s a new feeling.
"I think I was appreciated by the fans at my previous clubs but they never used to chant my name. But I guess it shows that the fans like me here and they like how I play.
"They like to see players that always give their all and that is what I do. I hope I can go on like that for the rest of the season."