The right-back impressed last season when on loan from Cologne and subsequently earned a long-term deal in May.
But Schalke now want to take Riether back to Germany and their ability to offer UEFA Champions League football could work in their favour.
However, the Bundesliga club's general manager, Horst Heldt, does not want to pay a big fee for the 30-year-old.
"If the asking price is too high, it will not happen," Heldt is quoted as saying in the Daily Star.
Riether made 34 appearances in the Premier League in the last campaign and was named Fulham's Player of the Season.