The Dane has made only three Premier League starts for Spurs this season under the management of Ange Postecoglou.
Hojbjerg has still featured 17 times throughout the campaign but he is not seen as a crucial player for the north London side.
Pape Matar Sarr and Yves Bissouma are preferred options in the Spurs midfield, so a departure could be set to take place next month.
Italian giants Juventus have Hojbjerg on their radar for the January transfer window, which opens in just under two weeks.
He is seen as a potential alternative to Kalvin Phillips, who looks set to leave Man City at the start of 2024.
READ MORE ON TRANSFERS
'Not good enough' - Havertz form may make United repeat emergency January transfer plan
Chelsea consider Ramsdale transfer after goalkeeper injury blow
However, it is not yet clear if Spurs will allow Hojbjerg to leave the club in the middle of the season.
The 28-year-old was speculated to depart in the summer transfer window as the club were willing to listen to offers.
Manchester United were linked with a shock move on the approach to deadline day but nothing materialised.
A switch to Juventus would see Hojbjerg join the side who currently sit second in Serie A as they chase their first league title since 2020.
Most read in Football
Ian Wright reveals real reason he is leaving Match of the Day
Former Tottenham boss candidate to replace under-fire Steve Cooper following shock talks
Van Dijk replies to Keane's arrogance claim after criticising Manchester United's tactics
Fulham to beat Man United, Liverpool and Arsenal to highly rated Brazilian in £20m+ deal
He would be competing for a starting spot alongside stars including Manuel Locatelli, Adrien Rabiot and former Leeds United loanee Weston McKennie.
Juventus are unable to offer European football for Hojbjerg but they have a very good chance of winning silverware in the Serie A or Coppa Italia.
Spurs fan believes Tottenham players need more discipline following continuous suspensions
The midfielder joined Spurs from Southampton in 2020 and has since made 162 appearances across all competitions for the north London club.
Most of Hojbjerg's appearances this season have come as a substitute and regular football is needed ahead of Euro 2024 in the summer.