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The photos were taken on Sunday, according to the Web site. TMZ did not specify which city the photos were taken in, 10TV News reported.
Many people, including 97.9 FM WNCI Columbus DJ Jimmy Jam believed the TMZ video showed her at the Old Navy store at the Lennox Town Center on Olentangy River Road.
Store officials refused to comment, 10TV News reported.
The Dave and Jimmy Show offered up to $10,000 to Anthony to take off the Ohio State University hat and wear Michigan attire.
Anthony has family in northeast Ohio, according to various media outlets.
Anthony was scheduled to appear in an Orlando courtroom on Thursday for a probation hearing about a check fraud charge.
Her attorney said that she would be in danger and need protection if she had to return to Florida.
Last month, Anthony was acquitted on charges that she was involved in the slaying of her daughter.