"I could say as an estimate that it could be at least a year," Jose Manuel Merino, the international affairs official at the attorney general's office, told Radio Formula.
But Merino warned that the process could last as a long as four to six years depending how hard Guzman's lawyers fight his extradition through injunctions.
Guzman's lawyer, Juan Pablo Badillo, has vowed to appeal to the Supreme Court if necessary.
Sean Penn interview helped 'Chapo' capture
Interpol Mexico agents went to Guzman's prison near Mexico City on Sunday to execute two arrest warrants for his extradition, formally launching the process. The foreign ministry would have to give the final green light after judges issue a ruling.
Mexico received the US extradition requests last year on a slew of charges, including drug trafficking and homicide. Guzman is wanted in half a dozen US states.
Guzman is now back in the same maximum-security prison he escaped from in July last year.
The drug lord was arrested in February 2014 but it only took him 17 months to escape from the Altiplano penitentiary after his henchmen dug a 1.5-kilometer (one-mile) tunnel to set him free.
Guzman was recaptured on Friday in a deadly military raid in Los Mochis, a northwestern seaside city in his home state of Sinaloa.
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