Riether has impressed since moving to Craven Cottage on a year-long loan from German side Cologne at the start of the season, with boss Martin Jol previously indicating his desire to keep him.
Jol is keen to trigger a clause in his contract to secure a permanent move and Riether and Riether told Fulham's official website: "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 added: "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 had never played outside of his home country until making the move to Fulham.
But the 29-year-old, who made his two Germany appearances in 2010, admitted he had felt at home straight away.
"In my mind, I've never thought of myself as being here 'on loan'," he said.
"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 Cologne player.
"For me, it's been a great time here so far. It was my first experience of another country and it was a big step for me to come to England. I have always played in Germany but this was an exciting challenge for me.
- Sports & Recreation