The 29-year-old joined Southampton from FC Twente in the summer of 2014, and has made 134 Premier League appearances for the Saints over the last four seasons.
Tadic scored seven times in all competitions last term, but the attacker is said to be unsettled in England.
According to Sky Sports News, negotiations between Ajax and Southampton are at an advanced stage, and an £18m move will soon be announced.
Tadic is currently in action for Serbia at the 2018 World Cup, and could help his team into the knockout round of this summer's competition in Wednesday night's clash with Brazil.
The attacker has previously been linked with a move to the Chinese Super League.