The report also said that if Hoyer -- who just completed his second season in his current post -- left the Padres, that San Diego vice president of baseball operations, Josh Byrnes, would be elevated to general manager.
Hoyer's current contract runs through 2013 with a club option for 2014.
"I'm proud of what we have accomplished so far and I'm excited about what we continue to build here in San Diego," Hoyer told XX-1090, the Padres' flagship radio station. "I'm busy interviewing hitting coaches today and I'm not going to comment on media speculation."
Byrnes was the general manager of the D-backs from 2005 until last season. It was Jeff Moorad, the Padres vice chairman and CEO, who hired Byrnes in Arizona and awarded him with an eight-year extension in 2008.
As for Hoyer, he joined the Red Sox in 2002 at the same time as Epstein. He was hired by Moorad as general manager in October 2009, replacing Kevin Towers.
Byrnes also worked as Epstein's assistant before becoming general manager of the D-backs, who advanced to the NLCS in 2007. Moorad awarded him with an eight-year contract extension in 2008. Brynes was dismissed in July 2010.
Moorad then hired Byrnes last December.
As for Epstein, his status remains in limbo as the Cubs and Red Sox continue to negotiate terms that would allow Epstein to officially be hired in Chicago.