The 34-year-old has fallen out of favour at Primera Liga champions Real and will be allowed to move on in search of regular football.
Carvalho was omitted from the Real squad which toured the United States this summer, sparking speculation that he could be on his way out of the club.
A return to England, where he has previously taken in a successful spell with Chelsea, was quickly mooted.
Tottenham were said to be keen on the experienced centre-half, who won three Premier League titles during a six-year stint at Stamford Bridge.
It is, however, QPR who have leapt to the front of the queue in the battle to bring Carvalho back to London.
Mark Hughes has made the acquisition of defensive reinforcements a top priority, having seen his side open the new season with a 5-0 home defeat by Swansea.
A deal for Spurs’ England international Michael Dawson is believed to be close to completion and he could be joined at the heart of Rangers’ back four by Carvalho.