And Norwich midfielder Leroy Fer – who came up against Vargas at the World Cup - is undergoing a medical ahead of his expected transfer.
Vargas, who scored a superb goal in Chile's victory over Spain in the World Cup, had been linked with a move to Arsenal and Sunderland.
But QPR boss Harry Redknapp now looks set to sign the 24-year-old on loan for the rest of the season, with the option of signing him permanently for £8million next summer. Vargas spent the second half of last season on loan at Valencia.
Netherlands international Fer, also 24, came off the bench for Norwich in their 3-0 win over Watford on Saturday, but he has talked about a return to the Premier League ever since the Canaries were relegated last season.
Redknapp revealed last month that Fer was one of his top targets for the rest of the summer transfer window.
Fer joined Norwich at the start of the 2013-14 season and scored three goals in 29 outings, going on to secure a place in Louis van Gaal's squad for the World Cup where he scored in their group clash with Chile after coming on as a sub.
Sky sources understand Fer will cost QPR in the region of £7.5million.
If the deals go through, the duo will become Redknapp's fifth and sixth signings of the summer transfer window.
They will join Rio Ferdinand, Steven Caulker, Mauricio Isla and Jordon Mutch as new faces in the squad.
Redknapp told Sky Sports News HQ: "Vargas is a quality player – he is sharp, he is bright. He can play up front, he can play as a No 10. I liked him in the World Cup and he's someone we've been following for a while. So we're hoping it's a possibility that we can bring him in.
"We've had reports on him for quite a while. One of our scouts who lives abroad has been following him for years now. It’s not done yet, but hopefully it is going to be done."
And on the imminent capture of the combative Fer, he added: "He will be an excellent signing – a Dutch international who played in the World Cup. He is an outstanding midfield player and will bring a lot of qualities to the club.
"He's got a great physique, gets box to box - I think he'll be a good signing for us. We were a bit light (in midfield). You need cover everywhere."
Redknapp confirmed that he would like to bring back Niko Kranjcar to the club. The midfielder spent last season on loan at QPR, having previously played under Redknapp at Portsmouth and Tottenham.
And Redknapp is hoping that Kranjcar can return if a deal can be done with his club Dynamo Kiev.
"He's a player I'm speaking to the chairman about. He's a Premier League player, real quality, who can do things other players can't," Redknapp said.
"He can see a pass and score a goal out of nothing. He's a great lad and a good professional so yes I'd like to get him back here. But we'll have to wait and see."