The Daily Star says both west London clubs are watching the 26-year-old, who has two-and-a-half years left on his AZ Alkmaar contract.
Moisander won the Dutch title with Alkmaar in 2009 and now captains the club, but is keen on a move to the Premier League.
He can play either as a centre-half or left-back, areas QPR and Fulham have identified as a weakness.
He said: "This is my fourth season here and I think it would be better if I find a different challenge. I'd love to play in another league."