Ronald Koeman is said to have retained his interest in the Dutch international since earlier in the season
And the Feyenoord captain revealed after the club's final game of the season against Heerenveen that his days in Rotterdam may be numbered, with the Star quoting him as telling the media: "Maybe this was my last game for Feyenoord. It is possible I might leave."
Koeman, of course, is familiar with the young midfielder after working with him during his spell in charge at De Kuip.
The Saints boss has already successfully recruited Graziano Pelle from Rotterdam since taking over at St Mary's last summer, and 23-year-old Clasie would be another Eredivisie star looking to make the step to the Premier League via Southampton.
Though the South Coast club will be reluctant to make too many squad changes after last summer, they may receive a couple of difficult to refuse bids for star players like Morgan Schneiderlin, and will see the season just gone as proof Koeman has what it takes to replace the side's outstanding players utilising his knowledge of Dutch football.
Clasie, who was a member of the Dutch World Cup squad and has 11 international caps to his name, may well be someone that either comes in alongside or in place of, the Saints' midfield star.