It is suggested that the decision of manager Mauricio Pellegrino comes a direct result of the recent record signing of Mario Lemina from Juventus.
Clasie, who joined the Saints from Feyenoord in 2015 after following Ronald Koeman from Rotterdam to Hampshire, hasn't featured in the squad for either of the first two games of the 2017/18 Premier League season.
The 26-year-old has played 49 times for the club in that time, appearing in just 16 Premier League games during the 2016/17 campaign.
Initially linked with Manchester United before making the move to St Mary's, an early injury unfortunately set Clasie back soon after he arrived on the south coast and Southampton fans have arguably never seen the Haarlem-born star at his best.
It remains to be seen where the player might end up, but if Southampton receive a suitable offer in the 10 days of the transfer window that remain his exit might well be quite swift.
The fee that originally brought Clasie to Southampton was £8m.