The 28-year-old has spent the last three-and-a-half years with Spurs and was regarded as a first-team regular under former head coach Antonio Conte, who departed in March.
However, Hojbjerg has fallen down the pecking order since the arrival of new boss Ange Postecoglou, starting just two of his 11 appearances in all competitions so far this season.
Yves Bissouma and Pape Matar Sarr have been favoured in centre-midfield by Postecoglou, while the return of Rodrigo Bentancur following a lengthy injury layoff is expected to see the Uruguayan given regular first-team minutes over Hojbjerg.
Tottenham are allegedly looking to sign a new midfielder in the January transfer window, which could hinder Hojbjerg's first-team opportunities further, and the Denmark international has subsequently been tipped to seek pastures new in 2024.
However, a recent report claims that Spurs will only sanction a sale of Hojbjerg if they manage to find a midfield replacement.
Serie A side Juventus have recently been credited with an interest in Hojbjerg, who is believed to be one of a number of midfield targets on their radar as they prepare for life without suspended duo Paul Pogba and Nicolo Fagioli.
Man United, meanwhile, were linked with Tottenham's No.5 in the summer, but they ultimately prioritised the addition of Sofyan Amrabat from Fiorentina on an initial loan deal that includes an option to buy.
According to Corriere dello Sport, the Red Devils could reignite their interest in Hojbjerg in January and rival Juventus for the midfielder's signature.
The report add that Atletico Madrid are also interested in Hojbjerg, who is under contract at Tottenham until the summer of 2025.
It remains unclear as to whether Man United, Juve and Atletico would prefer to negotiate a loan or permanent transfer for Hojbjerg, who is said to be valued by Spurs at around £30m.
Juve are believed to be working on a tight budget amid financial concerns and may look to sell a few of their key players to raise funds for new recruits, with the likes of Dusan Vlahovic, Federico Chiesa and Gleison Bremer having all been linked with moves away from the club.
As for Man United, it remains unknown as to how active Erik ten Hag's side will be in the winter window amid the ongoing uncertainty over the club's takeover.
Sir Jim Ratcliffe proposed 25% investment of the Red Devils is yet to be ratified, but a recent report claims that his purchase could be completed before the end of 2023.