The 32-year-old is reportedly unhappy at the Catalan club and will leave ad the end of June.
The report goes onto state that Alves will fly to Istanbul after this weekends UEFA Champions League final encounter with Juventus.
Galatasaray are understood to be preparing a €4.5 million per season deal for the Brazilian international.
Galatasaray ended the 2014-15 season with 77 points following their 1-1 draw with Rizespor in their final game of the season.
The Lions have become the first Süper Lig club to wear four stars on their shirt following the championship.
The Istanbul giants will qualify directly for the Champions League group stages next season.