According to the news outlet, the Chilean was in London for a medical on Wednesday and a deal for the Napoli man is expected to be announced soon.
The same report suggests Norwich City's Leroy Fer will also be confirmed as an Rs player very soon.
Vargas was linked with a move to Arsenal at one point this summer but now looks as though he will join up with fellow Chile international Mauricio Isla at Loftus Road.
Harry Redknapp will not be signing Jonathan de Guzman, however, who had been linked with QPR earlier this summer, as well.
The 26-year-old has been confirmed as a Napoli player after signing from Villareal.
De Guzman previously spent two seasons on loan at Swansea City.
Felix Magath's side will face Wolves at Craven Cottage tonight and Stafylidis was speaking to the official matchday programme.
“It’s a very attacking style here at Fulham,” he said. “We’re a team that keeps the ball well; possession is the key and it’s all about making the opposition work. We also press hard and break quickly if we can. The full-backs will play a big part in that system.
“I’m really looking forward to seeing how the campaign unfolds, because we have high hopes in regards to what we can achieve. I like to think I’ve played well in the games I’ve been part of, but there’s a lot more to come from me.
“First impressions are important; as a new player coming in, I want to do well and show what I can do. The Club has put a lot a lot of faith in me, and although I’ve only come in on loan, I want to assure the fans that I’ll give everything I have to help get Fulham back to the Premier League.”