A report published on Facebook on Saturday said Herman tipped college football reporter Brett McMurphy to look into Smith's relationship with his ex-wife Courtney and multiple allegations of physical abuse.
Herman, through a spokesman, said the report was "absolutely untrue" and denied that his wife, Michelle, contacted McMurphy either.
"Neither I, nor anybody in my family, has ever communicated with Brett McMurphy about the situation at Ohio State," Tom Herman said.
McMurphy also tweeted a denial that Tom Herman was a source in his reporting.
Herman did acknowledge that in March 2017 his wife offered Courtney Smith financial assistance but added they had "not provided any financial assistance since then."
Zach Smith was fired in July after reports about the alleged abuse. Ohio State is investigating whether coach Urban Meyer knew about a 2015 incident involving the Smiths and did not properly report it at the time.
Herman was Meyer's offensive coordinator at Ohio State from 2012 to 2014, while Smith was part of the offensive staff during that time.