The health of Mexican drug lord Joaquin "El Chapo" Guzman, one of the world's most notorious criminals, is deteriorating in US custody, his lawyers complained Monday, challenging the conditions of his detention.

The 59-year-old, accused of running one of the world's biggest drug empires and who escaped twice from prison in Mexico, has been held in solitary confinement in New York since being extradited on January 19.

His isolation at the Metropolitan Correctional Center in Manhattan has seen his "physical and mental health" deteriorate, wrote his American public defenders in a 24-page letter to the judge overseeing his case.

"He has difficulty breathing and suffers from a sore throat and headaches," they said.

"He has recently been experiencing auditory hallucinations, complaining of hearing music in his cell even when his radio is turned off."

His lawyers asked Judge Brian Cogan that Guzman be allowed to speak to his wife, either by person or by telephone, and be released from solitary confinement and placed in the general prison population.

Amnesty International has previously condemned conditions at the unit where he is being housed as "cruel, inhuman or degrading treatment and incompatible with the presumption of innocence," the letter said.

It is not the first time his legal team has complained about the draconian conditions of his incarceration.

They did so at a court hearing in Brooklyn on February 3, when Cogan declined to intervene at the time, saying it was up to the jail.

US authorities are adamant that Guzman will have no chance of freedom.

The letter said Guzman was confined to "a small windowless cell" where he remains alone, except for an hour of solitary exercise in another cell with a treadmill and stationary bicycle Monday to Friday.

His meals are passed through a slot in the door and the light is always on, it said.

Guzman shivers from a lack of warm clothing and never goes outside, the lawyers added.

On January 20 Guzman pleaded not guilty to a raft of firearms, drug trafficking and conspiracy charges at an initial hearing in New York.

If he stands trial and is convicted, he is likely to spend the rest of his life in a maximum security US prison.

Prosecutors are also seeking to obtain a $14 billion criminal forfeiture order against him.