Defender Jonathan Spector has extended his stay at Birmingham after penning a new two-year deal.
Bastian Schweinsteiger’s Bayern Munich future remains in doubt after Matthias Sammer admitted he could leave the club.
The right-back's parent club Cologne, relegated from the Bundesliga last year, say Riether will go elsewhere even if Fulham do not take up an option to sign the 29-year-old permanently.
"Fulham has the chance to buy him at the end of the season," Cologne executive Jorg Jakobs told Express. "Even if they do not pursue their buy-out option, there will definitely be another club signing him then."
However Riether's agent Volker Struth feels that there is a chance of his client returning Cologne.
"We were caught by surprise by Cologne's statements. As it stands, Sascha would have to return to the club for pre-season."
The twice-capped German international has started all 25 of the Cottagers' Premier league games so far this season, with manager Martin Jol recently saying that Riether had done a "great job" so far.
"I only wanted him on loan because you never know how they'll do," Jol declared in January.
"If he carries on like this we will make our mind up and try to extend it or buy him."