The experienced Barcelona midfielder has announced his retirement from international football following Spain's World Cup exit.
While he has made a decision on his international career, his club future remains uncertain, with his Barcelona contract set to expire at the end of the season, and he is believed to be attracting interest from the MLS.
Barcelona have already begun their search for a replacement if Busquets does leave, and according to Sport, they are considering a move for Varela.
The 21-year-old trained at Barcelona's soccer school in Buenos Aires, before he went through the Boca Juniors academy.
The Argentinian side have allegedly set an asking price of €20m (£17.4m), but Barcelona could face competition from Benfica, with the Portuguese side lining up Varela as a replacement for Enzo Fernandez, who has recently been linked with a move away.
Varela has four years remaining on his contract, and he has made 76 appearances for Boca Juniors, chipping in with one goal and three assists.