Hojbjerg has not been among the first-choice starters in pre-season under new manager Ange Postecoglou so far.
Yves Bissouma has been preferred in the holding role, while Oliver Skipp has also started ahead of the Dane in the centre.
Therefore, 90min claims that Spurs are now keen to push on with finalising a deal that would see Hojbjerg depart the club.
Spurs initially valued the midfielder - who turns 28 this week - at £40m, but without many suitors at that valuation, the club may compromise.
With the club not looking to stand in his way if Hojbjerg decided to depart, Atletico appear to be the front runners.
Diego Simeone is on the hunt for a new all-action midfielder, with Hojbjerg and Sofyan Amrabat both having been linked.
However, with Amrabat's most likely destination looking to be Manchester United, a move for Hojbjerg looks most probable.
It is believed that the Spanish club will not pay any more than £30m for the player though, so talks are set to continue.
That would still see Spurs double their money on the player though, after spending £15m to buy Hojbjerg from Southampton in 2019.
The Danish international has made 145 appearances for the club across those three seasons, and he has missed just five Premier League games in that time - two of which came at the end of last season.
Atletico have been suffering from a shortness of numbers in the centre of the pitch so far in pre-season.
The more technical and attack-minded duo of Thomas Lemar and Koke have started all three friendlies, while Saul Niguez has only had a bit-part role so far.
Axel Witsel is often used as a central defender now, and Marcos Llorente is reportedly on the verge of a move to Saudi Arabia, so a replacement is on the agenda for Simeone.