"We appreciate the devotion, passion and love that he [Osorio] showed in his work and in the preparations for every game of the national team, as well as his sincere and honest decision not to aspire to the position of the head coach for the next World Cup," the federation said in a statement.
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Earlier, the news website goal.com reported that Osorio decided not to extend his contract with the Mexican national team, and that he was being offered a job by at least six national teams.
Osorio was coaching the Mexican national football team since 2015, leading them to the fourth place at the 2017 FIFA Confederations Cup and to the top of the 2018 FIFA World Cup qualification group for the first time since 1997.