Goal understands that the Premier League champions have targeted a summer move for the Belgian centre-back, who has impressed since moving to St Mary’s from Atletico Madrid on a short-term deal.
The Saints have the option to sign Alderweireld permanently for £6 million at the end of the season but Atleti could cancel that clause by paying a £1.5m fee – thus giving them the option of selling the 26-year-old to the highest bidder.
Alderweireld, though, says that he would like to remain at St Mary’s, despite conceding that the decision ultimately lies with the Spanish champions.
“If I could choose then of course I would like to stay here,” he told BBC Radio Solent.
"It's not up to me. Atletico could decide that they want me back. I have two years left there so it is difficult for me to answer the question.
"I'm enjoying the Premier League, I'm enjoying playing for Southampton - I love the club and I love the supporters.
"We'll see, I am enjoying it here and my mind and focus is on Southampton."