Guzman managed to escape from jail in July 2015, much to the embarrassment of Mexican authorities.
It is likely he could be extradited to the United States early next year.
His lawyers have filed appeals to block the transfer. His lawyer Andres Granados has filed lodged papers in Mexico City.
He believes the court could take six months to issue its ruling, which will likely be appealed to the Supreme Court.
He said: "We know it's a high-profile case, which is very complex because it has to do with Mr Guzman."
The Mexican government has said the Sinaloa drug cartel leader could be extradited to the United States by January or February.
Guzman is facing two extradition bids, one in California for drug distribution and another in Texas on charges that include murder and money laundering.
Approving the extradition in May, the foreign ministry said in a statement that the US government had given "enough guarantees that the death penalty will not be applied".
Mexico, which has no capital punishment, has previously criticized the execution of Mexican nationals in the United States.
Another Guzman lawyer, Jose Refugio Rodriguez, said the guarantee is not ironclad because it was issued by the US embassy, whose real function in the matter is 'only to present' the extradition document.
The drug lord was recaptured in January, six months after his brazen escape from the Altiplano maximum-security prison through a one-mile tunnel that opened in his cell's shower.
He had previously escaped from another prison in 2001 and was arrested in 2014.
He was taken back to Altiplano after his January arrest, but was abruptly transferred in May to a prison in Ciudad Juarez, a city bordering Texas.
Guzman's extradition would lead to a major drug trial for the head of a cartel accused of providing tons of drugs to addicts in the United States while fueling violence in Mexico.
President Enrique Pena Nieto had balked at extraditing Guzman before his July 2015 escape, preferring to put him on trial in Mexico.
But Pena Nieto changed his mind after Guzman was returned to prison.