The 28-year-old is facing an uncertain future in North London having fallen down the pecking order under manager Ange Postecoglou.
Hojbjerg has starting just five of his 21 appearances for Spurs in all competitions so far this season, including only four starts in 15 Premier League outings.
Pape Matar Sarr and Yves Bissouma have been favoured in centre-midfield by Postecoglou, while the return of Rodrigo Bentancur from injury and the renaissance of Giovani Lo Celso in recent weeks has also hindered Hojbjerg's first-team minutes.
Hojbjerg, who is under contract at the Tottenham Hotspur Stadium until June 2025, has therefore been tipped to seek pastures new in search of regular game time.
Recent reports have suggested that Juventus hold an interest in Hojbjerg, but the Serie A leaders are understood to have pulled out of the race for the Denmark international for financial reasons.
However, according to Football Insider, a potential move for Hojbjerg to Juve cannot be completely ruled out, and a switch to another club also remains on the cards, but the Turin-based outfit have baulked at Tottenham's initial demands regarding a loan fee.
The report adds that Spurs will only sanction an exit of Hojbjerg if they find a midfield replacement during the January transfer window.
Tottenham's recent transfer strategy has primarily been to recruit players under the age of 24, and it is believed that they will stick to the same policy this month if they decide to step up their hunt for a new midfielder.
Spurs spent around £200m on nine players in Postecoglou's first transfer window at the club last summer, with seven of those players aged under the age of 24 - the exceptions being 26-year-old duo James Maddison and Guglielmo Vicario.
Postecoglou is set to bolster his squad further with the addition of 21-year-old central defender Radu Dragusin, who is allegedly closing in on a permanent transfer to the white side of North London.
A recent report claims that Tottenham have reached a full agreement with Italian club Genoa to sign Dragusin for €25m (£21.5m) plus add-ons, while Djed Spence could move in the opposite direction on loan.
Meanwhile, Spurs have completed the signing of former Chelsea forward Timo Werner on an initial loan deal from RB Leipzig until the end of the season, with an option to sign the 27-year-old permanently for around £15m in the summer.