Rs boss Harry Redknapp recently spoke of his desire to boost his forward line, with Charlie Austin one of just three recognised strikers at Loftus Road alongside Championship play-off hero Bobby Zamora and Remy, who spent last season on loan with Newcastle.
And it seems the Premier League club are close to landing Sigthorsson, who switched to Ajax from AZ Alkmaar for £4million in 2011.
The 24-year-old scored 12 goals in 42 games last term as the Dutch outfit claimed their third successive Eredivisie title.
Ajax director of football Marc Overmars is quoted as saying by the Daily Express: "I've had some good discussions with QPR about Kolbeinn, and the two clubs are close to agreeing a fee.
"Of course what the player wants is also important, but QPR are a good club for him."
Meanwhile, Redknapp wants Remy to make a quick decision on his future after his proposed move to Liverpool fell through.
The QPR boss told the Daily Mirror: "We need to know if he's going to stay or not, because we can't lose him on transfer deadline day and then not have a striker.
"If he's going to stay, we need that commitment now."