Atlético reportedly value Álvarez at his €500 million buyout clause and have shown no interest in negotiating a sale.
Arbeloa's departure comes less than six months after he was promoted from Castilla to replace Xabi Alonso.
Feyenoord's leadership concluded that a change was necessary following an extensive review of the team's progress and results.
Pérez's victory came in Real Madrid's first contested presidential election since 2006.
It follows a seven-month investigation coordinated by Europol and national authorities.
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