The story claimed a group led by Bush, and including Venezuelan media giant Gustavo Cisnero, made a "large offer" to buy the Marlins earlier in the offseason. The Herald story added that during the offseason, about a half-dozen people have expressed interest in buying the Marlins.
Loria, 72, assumed ownership of the Marlins in 2002. The team won the World Series in 2003. But in their first season at Marlins Park in 2012, they finished 69-93.
The paper added that if Loria opted to sell, it could possibly be after 2014, when the team would not be obligated to share profits with Miami-Dade County.
Joe Frisaro is a reporter for MLB.com. He writes a blog, called The Fish Pond. Follow him on Twitter @JoeFrisaro. This story was not subject to the approval of Major League Baseball or its clubs.