The 25-year-old Chilean international, who is on loan from Italian club Napoli, was hurt after scoring the opening goal in the 4-1 victory at West Bromwich Albion on Saturday.
The struggling Premier League club said earlier on Monday that Vargas would be out for 10 to 12 weeks, meaning he would miss QPR's last seven league matches of the season.
But his agent Cristian Ogalde said he was in daily contact with the QPR doctors who told him Vargas should be fit within six weeks.
"The information I have I was given directly by the doctor, with whom I am speaking every day, as well as with Eduardo," Ogalde told Chilean Radio Cooperativa.
"He shouldn't have any problem being at the Copa America but now it's evidently more important for him to even manage to play (some of) what remains of the Premier League."
QPR are second from bottom, three points behind Aston Villa who are two places above them and host Rangers on Tuesday.
Chile is hosting the Copa America from June 11-July 4.
(Additional reporting by Manuel Farias in Chile, writing by Ed Osmond/Rex Gowar, editing by Ed Osmond)
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