The appointment is to be announced Thursday, the newspaper reported. It said neither Purdue nor Daniels' office would confirm his selection.
Daniels, 63, is in his second term as governor and appointed eight of the 10 members of the current Purdue board. He leaves office in January.
While Daniels graduated from Princeton University and has a law degree from Georgetown, his career has been in business and politics. He headed the U.S. Office of Management and Budget during President George W. Bush's first term.
France Cordova, an astrophysicist and Purdue's first female president, plans to step down July 15. An interim will head the school for the next few months.
Purdue has almost 40,000 students. In addition to the flagship campus in West Lafayette, the university has five satellite campuses around the state.
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