Catania left back Vargas, 24, is widely regarded as one of the best in the business, and his performances for The Elephants since joining from Colón de Santa Fe in 2006 have reportedly attracted an array of admiring clubs.
Latest reports from Spain claim that Real Madrid are once again in the fray after supposedly going cold earlier this month.
The Spanish giants are believed to be interested in a more experienced option for the left side of their defence, to complement the more attacking option they have in Marcelo.
Coach Bernd Schuster wants to use Gabriel Heinze as a centre-half next season, so a spot has opened in the squad.
Vargas has already agreed terms with Real Madrid according to Sport, and the Merengues must now find an agreement with Catania. It is understood that a fee worth €15 million will be necessary to convince the Sicilians to off-load their star.
"He is a top-level player and quality in his position is not in plenty these days," said a Catania director, also recalling that the club refused to sell him last summer as well.
However, Real Madrid will have to fend off interest from the likes of Bayern Munich, AC Milan and Barcelona if they want to see the 24-year-old at Santiago Bernabéu next season.