The 29-year-old's loan deal from Koln will come to an end in the summer, but it is understood that Fulham have the option to buy the experienced right-back at the end of the season.
"I'd like to remain here. Fulham have an option to buy me and so I think in the next few weeks there will be talks about my future," he told the club's official website.
"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 has made 27 appearances in all competitions this season.