The 29-year-old, who has 54 caps for Serbia, will return to the Netherlands after scoring 24 goals in 162 appearances for Southampton, who narrowly escaped relegation from the English top flight last season.
British media reported that Southampton have agreed a fee to sign Norway playmaker Mohamed Elyounoussi from Switzerland's FC Basel.
Ajax finished second behind champions PSV Eindhoven in the top Dutch league last season.
Southampton goalkeeper Alex McCarthy has signed a new four-year contract.
The 28-year-old joined the Saints in 2016 but was primarily used in cup competitions before stepping up last season, featuring in the team's last 18 league matches.
"I think the club is going in the right direction. With the way we finished the season, we can take that into this one and hopefully finish a lot higher up the table," McCarthy said https://southamptonfc.com/news/2018-06-27/alex-mccarthy-new-southampton-four-year-contract-announcement on the club's website.
Manager Mark Hughes emphasised McCarthy's importance to the squad.
"His performances last season speak for themselves, and it is clear how highly regarded he is by his teammates and also the supporters," Hughes added. "We believe Alex is very much in the right place to continue to grow and improve his game."
(Reporting by Aditi Prakash and Arjun Panchadar in Bengaluru,; Editing by Keith Weir and Ed Osmond)
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