Hojbjerg has been a hit at the North Londoners since his arrival from Southampton in 2020, contributing 10 goals and 16 assists from 158 appearances in all competitions.
However, since Ange Postecoglou was appointed as the club's new head coach, the Denmark international has found himself down the pecking order.
Yves Bissouma and Pape Matar Sarr have been the Greek-Australian's preferred pairing in the middle of the pitch, leaving Hojbjerg as no more than third choice.
The 28-year-old has made a total of two starts and 10 substitute outings in the Premier League during 2023-24, accumulating a total of 435 minutes.
Having failed to appear in just one top-flight encounter, it has highlighted his value to the squad, yet he has consistently been linked with a transfer away from the Tottenham Hotspur Stadium.
Spurs would have been happy to cash in on Hojbjerg during the summer transfer window had they received their desired asking price, alleged to be in the region of £30m.
That never became a realistic possibility, subsequently resulting in Hojbjerg staying put, but interest is expected in his signature at the turn of the year.
Nevertheless, according to transfer expert Fabrizio Romano, club officials will give no consideration to parting ways with a senior player such as Hojbjerg on loan.
Juventus and Ajax have each been linked with a move for Hojbjerg in January as they bid to bolster their respective squads for the second half of the campaign.
Hojbjerg would also likely attract admirers from Premier League sides if it emerged that Spurs were content to adopt a soft stance regarding the manner of his exit.
Instead, any proposals for a temporary deal will seemingly be rejected out of hand, something which may not necessarily frustrate Hojbjerg at this time with Spurs in the Premier League title race.
With just over 19 months remaining on his contract, though, a sale in the summer is currently the most likely outcome as he contemplates a fresh challenge.