The veteran goalkeeper is weighing up his options as he seeks guarantees from manager Martin Jol about his likely involvement with the first-team next season.
Schwarzer has played in 36 Premier League games this season as the Cottagers finished 12th, and while the 40-year-old continues to defy his age, questions will remain about his ability to keep playing at the top-level for much longer.
Jol clearly rates the Australian, but he wouldn't be doing his job correctly if he didn't have one eye out for his eventual successor, and that uncertainty has left the ex-Middlesbrough man with plenty to think about as his existing deal runs out next month.
Riise said: "I hope Mark stays. He's kept us in a few games and did that against Swansea [Fulham's last game of the season].
"For half an hour we were forced to defend but he kept us in it and we scored a few more goals."