The Lilywhites are believed to be targeting a new centre-back for the second half of the campaign, despite Cristian Romero and Micky van de Ven's solid partnership under Ange Postecoglou so far.
The duo are significantly short of cover, though, as Davinson Sanchez left for Galatasaray permanently this summer, while Joe Rodon and Japhet Tanganga are on loan at Leeds United and Augsburg respectively.
Clement Lenglet's loan from Barcelona was not converted into a permanent deal either, despite some speculation, while Eric Dier is expected to depart in 2024 when his contract expires.
The Englishman represents the most senior backup option to Romero and Van de Ven, whose other deputies include 18-year-old Ashley Phillips and Ben Davies, who often played in a back three under Antonio Conte.
Spurs boss Postecoglou has hinted that his side will try to get some business done early during the January window, as new chief scout Rob Mackenzie and technical director Johan Lange prepare to start work at Hotspur Way.
Galatasaray and Denmark defender Nelsson had allegedly been identified as a possible target, and he could be available for a modest £26m in January owing to a clause in his contract.
However, a report from Football Insider states that Tottenham are not considering a winter move for the 25-year-old, in spite of his success in Turkey since leaving Copenhagen in the summer of 2021.
The 6ft 1in defender has two goals and one assist under his belt from 94 appearances in a Galatasaray jersey, playing 33 Super Lig games in the 2022-23 season as Galatasaray stormed to the title.
Nelsson has already played 14 times for the Turkish champions this season, although he was only a late substitute in their memorable 3-2 Champions League win over Manchester United and has started just one of their last six Super Lig contests.
The 25-year-old also has 10 Denmark caps to his name and was a part of his nation's squad for the 2022 World Cup, playing the full 90 minutes in a 2-1 group-stage defeat to then-champions France.
Nelsson's contract with Galatasaray runs until the summer of 2026, although his current club would be powerless to prevent him leaving should an interested party stump up his release clause.
While a move for the Dane appears to be a non-starter, Tottenham are believed to have earmarked a couple of other defensive targets in Borussia Monchengladbach's Ko Itakura and America's Sebastian Caceres.
A new centre-forward is also believed to be on Postecoglou's wishlist, as Richarlison has flattered to deceive once again this season, only finding the back of the net twice in 11 appearances.
However, Son Heung-min has shone in a central role with eight goals in 10 Premier League games so far this term, only sitting behind Erling Haaland (11) in the Golden Boot race.