(CNN)Joaquin "El Chapo" Guzman's complaining about lack of outdoor activity may be part of a plan to escape from detention before his sentencing next month, federal officials allege.

An attorney for Guzman this month asked a federal judge to intervene over "cruel and unusual" prison conditions for the drug kingpin detained in a federal prison in New York.

In the more than two years he's been detained, he's not had access to fresh air or natural sunlight, and is forced to put toilet paper in his ears to mask loud prison noise, his attorney wrote in a letter to the judge.

The United States issued a response to the allegations Thursday, saying the only outdoor exercise space at the facility is a rooftop with a wire mesh covering.