Seven women and five men were selected as jurors in the case against Joaquin Guzman.
Guzman formerly led the Sinaloa Cartel, based in the Mexican state of Sinaloa, which became one of the most powerful drug trafficking organizations in the world.
The names of the jurors will be kept anonymous under the strict security arrangements accompanying the trial.
Guzman, dressed in a blue suit and blue shirt, took notes and appeared attentive, but has otherwise been impassive during jury selection.
Cogan has yet to rule on the request.
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'It is well known that solitary confinement poses negative effect to a person's sanity, ' the filing, obtained by ABC News, stated. According to official court documents, "The only human contact Mr. Guzman has had since his extradition has been with the jail personnel when putting and removing his shackles, and a quick handshake from his attorneys when he goes to court".
Most of the people picked either for the jury or to serve as six alternates said in initial screening that they had heard of Guzman through news reports or TV shows.
The man, whose identity is withheld along with all potential jurors under the rigorous security arrangements surrounding the trial, was born in Colombia but has spent the last 20 years living in NY.
U.S. District Judge Brian Cogan, who is overseeing the case, said another woman told him privately, in tears, that her mother, with whom she lives, said they would have to "move and get a new house", drawing a laugh from Guzman.
Cogan also reported that one man, who was allowed to stay after being questioned on Monday, had asked a court officer if he could get Guzman's autograph.