One of Guzman's lawyers, Jose Refugio Rodriguez, told AFP that the Sinaloa drug cartel leader was "very serene" as he waits for the decision by a court in Mexico City.
The foreign ministry gave the green light to Guzman's extradition in May, but the former most wanted man won a temporary injunction in June, which the judge must decide whether to make permanent or strike down.
The hearing began before midday today, an official at the court told AFP.
If the judge approves the extradition, Guzman would have 10 days to appeal to a higher court of appeals, which would then take several weeks to rule, the lawyer said, warning that he would take the case to the Supreme Court if necessary.
A US government official told AFP on condition of anonymity that Guzman could be in US custody before the end of the year. He faces charges ranging from murder to drug distribution in courts in Texas and California.
After he was recaptured in January in his northwestern home state of Sinaloa, he was sent back to the same prison.
But he was abruptly transferred in May to another prison in Ciudad Juarez, a city bordering Texas that was once the scene of brutal turf wars between his gang and a local cartel.
Pena Nieto had balked at extraditing Guzman before his escape in July 2015, preferring to put him on trial in Mexico.
Refugio Rodriguez said his client's health has "deteriorated a lot" while in prison.
"He's doing very badly. He's isolated. He lost a lot of hair because he takes a lot of medicine. He lives in constant physical stress," the lawyer said.
He told Radio Formula later that his client's segregation amounts to torture and that evidence would be presented in court to improve his conditions. Guzman has complained in the past of being awakened by guards at night.
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