A website on the controversial Chinese voyages of discovery (Menzies "1421" book), states the following:
Investigations into the warrah, a thought-to-be indigenous, but now extinct fox or wolf-like animal whose origins are disputed. While DNA tests are carried out to resolve its ancestry, there are also tests being sought to argue for the warrah being descended from Chinese dogs left behind by Hong Bao's sailors (Whipple 2003: 80-1; Menzies 2002: 135). This research may take some time, considering that much doubt has been cast upon the whole theory by academics.
The paper mentioned is: Whipple, D. 2003. Histories: Alas, Poor Warrah. NewScientist. 20/27 December 2003 - 3 January 2004: 80-1.
See my original post on the Warrah.
Yet a recent paper by a team led by Graham Slater indicates that the warrah's closest relative is the maned wolf. They sampled DNA taken from the remains of Falkland wolves stored in museums and concluded that it shared a common ancestor with the maned wolf at least 70000 years ago. So, they had arrived to the islands long before there were any humans in Southern South America.
This was some time before the last ice age, so this rules out the theory of a domesticated dog being taken there from the mainland by native Americans in their canoes.
However, the Falklands wolf diverged from the mane wolf some 6 million years ago and that is long before the first Canids appeared in South America (2.5 million years ago). This means that they evolved in North America and then moved south.
Slater's team believes that their closest relative was the Dusicyon avus another Canid that became extinct some 7000 years ago.
 Slater, Graham et al. (2009). Evolutionary history of the Falklands wolf. Current Biology, Volume 19, Issue 20, R937-R938, 3 November 2009
Patagonian Monsters - Cryptozoology, Myths & legends in Patagonia2010 International Year of Biodiversity Copyright 2009-2010 by Austin Whittall ©