The goalkeeper's contract expires next month, and the Australian is thought to be considering his options unless he feels that he will remain as first choice next season.
Schwarzer started 36 league games this season as Fulham limped to a 12th-place finish, and the 40-year old was the second oldest player in the Premier League this season.
The goalkeeper's Norwegian team-mate Riise hopes that Schwarzer and Fulham can sort out a deal for him to remain at the club.
"I hope Mark stays," Riise said.
"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."
Schwarzer has made 172 Premier League appearances since his move from Middlesbrough in 2008.