That leaves manager Ronald Koeman with a huge gap to fill in his defence - and The Sun believe it's van Dijk who Southampton will pursue as Alderweireld's replacement.
The 24-year-old has been nothing short of superb ever since joining Celtic from Groningen back in 2013, but the time may be right for him to test himself in the Premier League.
Inadvertently, Alderweireld's move to Tottenham now poses Celtic's biggest threat of losing van Dijk, with Southampton an ideal destination for the Dutchman.
Working under compatriot Koeman would no doubt be an attractive proposition for van Dijk, whilst moving to the Saints would still give him the chance to play first team football on a regular basis, given Alderweireld's departure.
His height and strength make him a formidable defender, whilst he also has the ability to bring the ball out of defence, just as Alderweireld did during his time with Southampton, meaning that whilst he may not be a like-for-like replacement, he could still bring some similar attributes.
For Southampton, they have added young defenders to partner Jose Fonte in the last two summer transfer windows, and van Dijk would be an ideal candidate to follow in the footsteps of Alderweireld and Dejan Lovren before him, given that the Portuguese international could help teach van Dijk and help him develop into a more rounded defender.
Southampton have also raided Celtic in the last two summer windows, bringing Victor Wanyama and Fraser Forster to the South Coast - so they would have no reservations about signing a player from Scottish football and making them a key player.
A move to Southampton seems perfect for van Dijk - and if the reports are correct, Celtic should be worried about losing their star player this summer.