The right-back is contracted with Liverpool until the end of June, when he will become a free agent.
Real Madrid’s opening game is against Al Hilal, who have a strong interest in signing Mohamed Salah if he leaves Liverpool, on June 18 in Miami.
FIFA is also allowing national associations of Club World Cup participating clubs to open a special transfer window between June 1-10 to sign and register players.
Clubs can also add a maximum of two players to their squad during an in-tournament window between June 27 and July 3.
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“If they want him to play in the group stage of the Club World Cup, they are going to have to negotiate with Liverpool and come to some arrangement for him to be released early from his contract,” said Sky Sports News chief reporter Kaveh Solhekol.
“They could say ‘we’re going to wait until July, we don’t need him for the group stage’.
“But Alexander-Arnold hasn’t told Liverpool he wants to leave, Real Madrid haven’t told Liverpool they have come to an agreement to sign him when his contract runs out.”
Liverpool’s final game of the season is against Crystal Palace on May 25.
Alexander-Arnold could also feature for England against Andorra on June 7 and Senegal on June 10.
Will Ronaldo be at the Club World Cup?
A big question also remains as to whether Cristiano Ronaldo will sign a short-term contract to play in the tournament.
At 40, he is unlikely to be able to play in the next tournament in 2029. He is out of contract with Al Nassr this summer – and they have not qualified to take part this year.
His great rival Lionel Messi is set to play after Inter Miami were given a slot by FIFA.
