Carlo Ancelotti is an admirer of Hojbjerg and came close to signing the Dane when he was in charge of Everton but was beaten to the punch by Spurs, who made a late move.
Spurs are under no real pressure to sell Hojbjerg unless he pushes for a move away. He has three years left on his contract in north London.
The Spanish giants are yet to make a move for the 27-year-old, but Spurs manager Antonio Conte is likely to demand a replacement if Madrid follow through on their interest.
Hojbjerg has been a key player for Spurs since joining from Southampton in 2020 for a fee of around £15 million.
However, he may have his head turned if the Spanish champions come calling when Casemiro completes his move to Manchester United.
Casemiro’s move to United was confirmed by Fabrizio Romano, who reported that the Red Devils will pay an initial €60m plus €10m in add-ons for the 30-year-old defensive midfielder. He would sign a four-year deal at Old Trafford.
Hojbjerg joining Madrid cannot be completely excluded, but it is unlikely he will move this summer as Madrid are not likely to sign a replacement for Casemiro.
It is safe to say Madrid had already planned for a transition in midfield when they signed Aurelien Tchouameni from AS Monaco earlier in the transfer window.
With Luka Modric, Toni Kroos and Eduardo Camavinga already in the squad, Hojbjerg would struggle to get enough action ahead of the World Cup in Qatar.
Tchouameni started Madrid’s 2-1 win over UD Almeria in their season opener, and Casemiro’s impending departure means the Frenchman is set to take over reigns in the middle of the park.
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