The pair would have to pay a seven-figure fee for the Dutch second division player, according to a report.
Dumfries, 19, is reportedly valued at £1 million by Sparta.
The right-back, who can also operate anywhere across the back four and as a defensive midfielder, has starred in his first full season for the Dutch side - helping them to the top of the second-tier Jupiler League.
Swansea are well-stocked in Dumfries' position, but with Angel Rangel's contract expiring in 2017, the Welsh side are likely to be eyeing up younger alternatives.
On the other hand, James Perch is the only specialist right-back currently on QPR's books, though others such as Nedum Onuoha and Grant Hall can play there if required.
One thing that could scupper the R's hopes of landing Dumfries is the club's sizeable debt, which now stands at £193 million according to a report by the Times.
Dumfries was previously called up to the Netherlands' Under-20 squad, but has since switched his allegiance to Aruba, for whom he has won two caps to date.