Marquez, 39, took a nearly three-month break from football after the US Treasury Department accused him last August of being a "front person" for a drug trafficking group based in the Mexican city of Guadalajara.
"Off the pitch, there's no debate, he's the footballer who can bring the most to this team," he said.
Marquez, who will be playing in his fifth World Cup, was included in the squad as a midfielder rather than a defender.
Brothers Giovani and Jonathan dos Santos, who both play for the Los Angeles Galaxy, were also named as midfielders.
He plans to announce his final list of 23 players on June 2, after Mexico's farewell home match, a friendly with Scotland.
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