Sigthorsson has an impressive goalscoring record with 15 goals in 23 internationals and 24 in 59 games for Ajax.
QPR boss Harry Redknapp wants to boost his striking options ahead of their return to the Premier League.
Sigthorsson, 24, spent a year with AZ Alkmaar before joining Ajax in August 2011.
Reports in the Dutch media had suggested that the 6'1" striker was being targeted by Swansea, but QPR look set to beat them to the signing.
Triffic striker of the ball, bags of energy, he'll be a top top addition. A Mikeal Forsel stature of a man.- dannyjohnson