The 58-year-old head of the Sinaloa cartel is thought to have been among the bodies left after the shoot-out in a remote rural area of Peten, in Guatemala.
Residents who witnessed the clashes have told authorities that one of the two dead men resembled the Mexican drug baron.
Police and soldiers are to search the area in an attempt to locate the scene of the fight on the border with Mexico where drug violence has increased.
Joaquín Archivaldo Guzmán Loera, also known as “Shorty Guzmán” because of his 5ft6in height is one of America’s most wanted criminals.
He has been the most powerful drug lord since his rival was captured in 2003 and since 2009 has been named every year by Forbes as one of the world’s most powerful people with an estimated fortune of $1bn.
Last week he was named Chicago’s Public Enemy No 1, a name not given to any criminal since Al Capone.
JR Davis, president of the Chicago Crime Commission, said: “Not since the Chicago Crime Commission’s first Public Enemy No. 1 has any criminal deserved this title more than Joaquín Guzmán.”
Chicago is one of the Sinaloa’s most important cities both as a place to sell drugs but also as a hub to distribute them across the US.
The US sees him as such a threat that it has put a $5m reward for information leading to his capture.
The Drug Enforcement Agency believe he has surpassed the infamous drug lord of the 1980s, Pablo Escobar, in terms of both his notoriety and the scale of his operation.
He has been in hiding since escaping from a Mexican prison in a laundry cart in 2001.
If he has been killed in a gun battle, it will be a significant boost to America’s battle against drugs, although another Sinaloa head will be ready to take his place.
Interior Minister Mauricio Lopez Bonilla said that police and soldiers would begin searching the area on foot and in the air at first light today.
However, the authorities have stressed they had only received reports of the battle from local people.
Government spokesman Francisco Cuevas told Guatevision Television that two drug gangs had clashed in Peten.
“We have to wait for all the technical information in order to determine if, in fact, one of the dead is of Joaquín “El Chapo” Guzmán,” Cuevas said.
Interior Department spokeswoman Carla Herrera said that one of the victims physically resembled the drug lord.
She said officials had asked the Mexican government to send Guzmán’s fingerprints to compare them to the man found inside a vehicle and to send investigators.
Mexican President Enrique Pena Nieto said late Thursday that he had no information on the case.
He said: “I don’t have any information that can confirm that.
Peten province is an isolated area of jungle and ranches where 27 ranch workers were massacred in 2011 by the Zetas drug gang, a top rival for Guzmán’s Sinaloa drug cartel.
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