Despite landing a number of high-profile signings this summer, QPR began their season with a 5-0 home loss to Swansea on Saturday.
The defeat, which came in front of Hoops owner Tony Fernandes, looks to have convinced Rangers boss Mark Hughes that he needs defensive reinforcements and the Welshman has reportedly agreed a season-long loan deal with Real Madrid to sign former Chelsea defender Carvalho.
Carvalho enjoyed six successful seasons at Stamford Bridge before moving to the Spanish champions in 2010, but he is now surplus to requirements.
The 34-year-old Portuguese may complete his move to Loftus Road before the end of the week and Dawson could also become a QPR player in time for Saturday's game at Norwich.
Although Dawson is Tottenham's club captain, new Spurs manager Andre Villas-Boas has decided that the England international can leave for QPR, who had a bid accepted for the player on Tuesday.
It is believed Dawson, who signed for Tottenham in 2005, will discuss terms with QPR in the next 24-48 hours.
The fee agreed between the two clubs is understood to be between £5.5million and £10million.
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