Tadic has spent four years with Saints, scoring 23 goals from 162 appearances in all competitions after joining from Eredivisie club FC Twente in 2014.
He played in 36 of the south-coast club's top-flight games last season, bagging himself six goals as Mark Hughes managed to keep them in the Premier League.
However it was reported earlier in the week that he may be sold this summer, with Amsterdam giants Ajax said to be the club interested in his signature.
Koeman, who assisted his brother Ronald at St Mary's for a couple of years, feels it would be a great signing both for the club and football in the Netherlands.
"For Dutch football it's great that such a boy comes to play in the Eredivisie," he told De Telegraaf. "If a club succeeds, it is worth a compliment. Dusan is a top professional and a good person, a huge enthusiast. Ajax gets a fantastic player in every respect."
However, the 56-year-old tactician admitted it was a shock to learn of the rumours, adding: "It surprises me that he returns to the Eredivisie, because he has renewed his contract with Southampton in the meantime and earns money there, which he normally will never be able to get at Ajax."