The 33-year-old is currently a free agent after leaving the Cottagers at the end of last season.
While suggesting that Villa are keen on his services, Riise is also being tracked by clubs in Spain.
"There has been some interest from a few English clubs," he told VG. "Aston Villa is one of them. There has been some interest from Spain also, but there is nothing on the table yet."
Riise made 25 appearances in all competitions for Fulham last season.