Alex Cifuentes, who says he was a close associate of Guzman for years, told a New York City courtroom that he had told authorities of the bribe in 2016.
Guzman is accused of being behind the Sinaloa drug cartel, which prosecutors say was the largest US drug supplier.
Mr Peña Nieto served as the president of Mexico from 2012 to 2018.
Mr Guzman, 61, has been on trial in Brooklyn since November after he was extradited from Mexico to face charges of trafficking cocaine, heroin and other drugs as leader of what the US has called the world's largest drug cartel.
According to reporters in the Brooklyn courthouse, Mr Peña Nieto had requested $250m before settling on $100m.
Cifuentes claimed the delivery was made to Mexico City in October 2012 by a friend of El Chapo.
Cifuentes, a Colombian drug lord who has described himself as El Chapo's "right-hand man", worked as his secretary and spent two years hiding from authorities with him in the Mexican mountains, according to prosecutors.
He was arrested in Mexico in 2013 and was later extradited to the United States where he pleaded guilty to drug trafficking in a deal with prosecutors.
Mr Peña Nieto has not responded to the latest claim, but has previously rejected allegations of corruption that have surfaced during the trial since it began in November.