The Spanish right-back was something of a cult hero at The Liberty Stadium and his release this summer has seen QPR take a recent interest. Steve McClaren's side have lost both of their Championship games and with Darnell Furlong out injured for three months, cover is required.
Rangel, 35, is thought to have been training with the west Londoners as the two parties try to iron out the finer details of a deal.
The ex-Swan isn't likely to sign passed the end of the season, but signing an experienced player like this will be a boost for QPR's younger players. With The Hoops restricted to loans and free signings until the summer transfer window, the full-back would be a sensible addition.
Osman Kakay has occupied the right-back position in Rangers first couple of Championship games and has performed admirably in both. It's unclear at this stage, however, if manager Steve McClaren will give Rangel an immediate starting berth, but Kakay is likely to have a fight on his hands to keep his place.
Rangel made over 300 appearances for the Swans scoring nine goals and registered 30 assists during his 11 year stay.