AC Milan and Tottenham failed with attempts for Real Madrid winger Marcos Asensio over the summer.
Marca says Real Madrid were prepared to sell the Spain international and considered the proposals from Milan and Spurs.
However, Asensio personally rejected both clubs in order to stay and fight for his place in coach Carlo Ancelotti's plans.
The winger still has an uphill battle to win over Ancelotti, with Gareth Bale, Eden Hazard and Vinicius Junior all ahead of him.
Adding to Asensio's difficulties is that he missed preseason due to his Olympics commitment.
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