The two are good friends from their time at Antwerp, Ajax and the Belgian national set-up.
The Belgian spent last season at St Marys and was in excellent form for the majority of the campaign, although did struggle with some injuries in parts.
The Daily Mail report that Daniel Levy has flown to Madrid to finalise a deal and that they have beaten Southampton to his permanent signing.
If he was to make that move, it would see him team up with a former club mate and current international comrade in fellow defender Jan Vertonghen.
Vertonghen, 28, joined Ajax from Germinal Beerschot Antwerpen in 2003 and went on to play for the club for nine years until joining Spurs in 2012.
Alderweireld, 26, also joined Ajax from Germinal Beerschot so the pair have known each other for a very long time.
They have also both been playing regularly for the Belgian national team together since Alderweireld made his Red Devils debut in 2009.
Both are former Ajax captains and Tottenham will hope getting the pair back together can see them rekindle an excellent defensive partnership and friendship.