Despite a "large offer" to buy the team, Bush became the latest of about a half dozen suitors to be turned down by Loria, the newspaper reported Wednesday.
The group of wealthy investors put together by Bush reportedly included Venezuelan media mogul Gustavo Cisneros.
Bush declined to discuss the report or if he would have been the Marlins' chief executive officer and managing partner if the team had been sold.
Under Major League Baseball rules, Bush could be the team's managing partner even if he owned only a small percentage.
After 2014, Loria, 72, would have more incentive to sell because he would no longer have to split profits with Miami-Dade County.