The 31-year-old has recently parted company with Olympiacos after just one season with the Greek giants.
Saviola was once a £15 million signing for Barcelona back in 2001, the journeyman centre-forward netted just short of fifty goals during his time at the Nou Camp, before going on to represent the likes of Monaco, Real Madrid, Benfica and eventually Olympiacos.
Harry Redknapp is eager to bolster his attacking ranks at Loftus Road, with Loic Remy on the verge of becoming a Liverpool player.
The fact that Saviola is available on a free-transfer could appeal to the 67-year-old QPR boss, who will be keen to learn from the mistakes that were made by the club two seasons ago, although it's likely that the Argentinian will require a relatively large pay packet.
Garry Monk is also looking to strengthen his side ahead of the new season, and with Gylfi Sigurdsson seemingly close to sealing a permanent move to the Liberty Stadium, Saviola would show that the Swans really mean business.
Fans of the Welsh side will hope any interest doesn't signal the club's intention to sell Wilfired Bony, but with the much-wanted Ivorian currently priced at £20M, he may well be linking up with Saviola next season.
The 31-year-old clearly still possesses a goalscoring touch, Saviola registered 14 goals in 34 appearances for Olympiacos last season, and on a free-transfer he may well turn out to be one of the bargains of the summer.
Do you think QPR or Swansea have a chance of getting Saviola?