Vietto joined Atletico Madrid just over a year ago, but only managed to make 19 La Liga appearances last season for the Champions League runners up.
The Argentinian striker enjoyed a good campaign with former club Villarreal in the 2014-15 season, scoring 20 goals in 48 games and has attracted attention from some of Spain's top clubs.
Barcelona are rumoured to be interested in the 22-year-old but Sevilla is the young forward's preferred option, as first-team opportunities may be limited at the Catalan club, given their strike force of Messi, Neymar and Suarez.