Tadic, who is currently away on international duty with Serbia at the World Cup, was key as the 'Saints' successfully avoided relegation to the Championshipo last season, sccoring seven goals in 41 games in all competitions to help the club keep its head above water.
However, the aforementioned source claims that the 29-year-old believes the time has come for him to return to Dutch football.
The Serbian spent four years in Holland earlier in his career, first with Groningen and then Twente before making the move to English football.
Having now spent four years at St Mary's, it is believed that Tadic has now set his sights on a new challenge, with a return to the Eredivisie seen as an interesting option.
Tadic has two years remaining on his current contract on the South Coast, but discussions with Ajax are thought to be well underway, with the player set on leaving the club before the end of the transfer window.