Harvin, now a professional playing for the Minnesota Vikings, played for the Gators from 2006-08.
He was one several team members who received preferential treatment while Meyer was the head coach and who were allowed to get away with poor behavior -- including physically attacking wide receivers coach Billy Gonzales, the publication said.
Citing multiple unnamed sources, the report said Harvin grabbed Gonzales by the neck and threw him to the ground in 2007, a year before Meyer led Florida to a second national championship.
Sporting News said Meyer's treatment of Harvin and other "favorites" contributed to an undisciplined climate that ultimately led to the team's crash.
Meyer resigned unexpectedly in December 2010 after the Gators fell to 4-4 in the SEC. They posted a 3-5 conference record last season under Will Muschamp, who was hired to replace Meyer.
Harvin didn't return calls for comment, the publication said.
"I am very proud of our guys that played at Florida," Meyer told SN. "Are there issues? Yes there are with 18- to 22-year-olds. I have been criticized that I have been too lenient on players; that doesn't concern me."