The Aston Villa man is available on a free transfer, and has previously starred for Ronald Koeman.
Southampton are facing up to the prospect of having to start the new season without two of their first choice defenders from the last campaign.
Ronald Koeman has already signed a ready-made replacement for Clyne in Portugal international Cedric Soares, and if he wants to invest elsewhere and pick up a top central defender to come in in Alderweireld's place, the Southampton manager could well look no further than Aston Villa man Ron Vlaar, a player Koeman knows very well and someone the Mail say the Saints are keeping an eye on.
A vital part of the Netherlands' charge to third place at the World Cup last summer, under Koeman, Vlaar had his best ever finish in the Eredivisie in 2011-12.
The Dutch defender's final season in the Netherlands was Koeman's first managing in Rotterdam, and the former Barcelona star took Feyenoord to second place in the division, just behind Ajax, who coincidentally, would have included Alderweireld in their ranks.
If he can inspire a similar spell of form at Southampton, then there are no better defenders available on a free transfer than the 30-year-old.
Would there be any drawbacks to Vlaar moving to St Mary's?
The Villa defender missed plenty of games last season with injury, and had a horror match against Sadio Mane at St Mary's at the end of the season, but if given a run of games injury free he could well be an astute signing.
Though he is an excellent defender, it could be argued that Vlaar and Jose Fonte are too similar. For the majority of last season, the Portuguese played along side Alderweireld or Maya Yoshida, both centre backs with a bit of pace to their game.
Though if Vlaar featured alongside Fonte, they would be positionally sounds and well organised, the duo would lack the acceleration to match runners trying to break past them.
Koeman could adjust his playing or defending style to compensate for this somehow, but he would surely be reluctant to change the strategy of what was the second best defence in the league last season, even if they do end up without two of the players that were part of that back line.