The midfielder has been heavily linked with a move to St Mary's since Adam Lallana left for Liverpool, and his current manager, Alfred Schreuder, has confirmed his imminent exit
Tadic has been linked with a move to St Mary's since Dutch coach Ronald Koeman replaced Mauricio Pochettino at the end of 2013-14 season.
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Now Tadic appears set for a switch to England's top flight after Schreuder confirmed the 25-year-old sat out Twente's 14-1 friendly win over amateur club VV Oldenzaal due to his proposed transfer.
"Everyone knows he is close to an agreement," Schreuder told newspaper TC Tubantia.
"We don't want to take any risks with him at all."
Tadic has flourished in the Eredivisie since initially joining Groningen from Serbian side Vojvodina in 2010, with the midfielder creating 483 chances in four years - 178 more than any other player in that period.
He also enjoyed his best season in 2013-14, scoring 16 goals in 33 league appearances for Twente - only forwards Aron Johannsson (17), Graziano Pelle (23) and Alfred Finnbogason (29) netted more.