According to Marca, Mourinho will lead Real Madrid's pre-season preparations starting on July 13.

Real Madrid fans have been waiting anxiously for weeks. Now, they finally have a date to look forward to: July 13. On that day, at the Valdebebas training ground, the whistle will signal the official start of José Mourinho's second spell as Real Madrid coach. With just over a month left until the team returns to training, Real Madrid will prepare for the new season. After two bittersweet seasons, the club and fans are both full of anticipation and high demands.
Mourinho himself has informed the team of this date. The Portuguese arrived in Madrid on the evening of June 9 Beijing time (CEST) and checked into the Hotel Santo Mauro. After a low-key arrival, he held his first meeting with club general manager José Ángel Sánchez, head scout Juni Calafat, and agent Jorge Mendes at 2:30 AM Beijing time (CEST) on June 10. On the very night Benfica announced his departure, this new project became unprecedentedly concrete both competitively and contractually. From today, Mourinho will move into Valdebebas, where he will have several weeks to calmly plan the framework for his second spell at Real Madrid.
The transfer market has already taken its first steps. Konate and Dumfries are the first two confirmed new signings, and they will reinforce a defense that has shown obvious problems over the past two seasons. Real Madrid had offered €150 million to sign a top superstar, which was also an important promise during the election campaign. Florentino Pérez's chosen target was Julián Álvarez, but the offer was rejected by Atlético, and the deal did not initially go through successfully.
The World Cup will conclude in the United States on July 19, which significantly affects Real Madrid's preparation plans. Ten first-team players have been called up to their respective national teams: Vinicius, Mbappé, Bellingham, Valverde, Courtois, Tchouaméni, Güler, Brahim Díaz, Rüdiger, and Endrick, who returns from loan and is on the team roster. Nico Paz might also join them; signs of his return to the club seemed to appear in a video during Florentino's campaign.
These players will have two to three weeks of vacation after participating in the World Cup, so their return to training will necessarily be staggered. However, most of the other players have a clear schedule: July 13, no excuses.
The overlapping World Cup schedule has also forced Real Madrid to readjust their pre-season structure. The club has ruled out plans for an international tour this summer; in previous summers, the team had traveled to the United States, but this model does not fit the schedule. Instead, there will be multiple friendly matches, including the Teresa Herrera Trophy against Deportivo La Coruña. Real Madrid needs to use these matches to get into shape for the first round of La Liga, which is expected to take place on the weekend of August 15. In any case, the countdown has begun.
