The 26-year-old midfielder is the younger brother of former Liverpool left-back John Arne Riise and has won 16 international caps.
In a brief statement Fulham said: "Norwegian midfield player Bjorn Helge Riise has travelled to London for talks with the club and is currently undergoing a medical examination.
"This process is not due to be completed until late on Tuesday evening."
Riise, who has spent the last five years at Lillestrom, is set to become Fulham's second summer signing following the capture of right-back Stephen Kelly from Birmingham City.
In 2003, Riise joined Standard Liege after a move to Cardiff City fell through. After one season he moved on to Brussels and then signed for Lillestrom in 2005.
Riise has scored six times in 15 appearances for Lillestrom this season.