There is no offer at present, Meyer, currently a college football analyst at ESPN, told the newspaper.
"I'm in a good place right now mentally and physically. So if something happens with Ohio State, I'll have a decision to make. But there has been no interview. There has been no offer to make a decision about," he said, according to the report.
Saturday, ESPN.com reported that according to sources, Ohio State and Meyer have been in contact about the job and that there was strong interest on both sides.
Meyer, whose resignation from Florida a year ago was fueled in part by health and family concerns, still has those concerns, he told the Sun. But in the past year, he's learned that a balance between the demands of coaching and home life can be found.
"I've found that it is possible to have balance between your job and your family, that there are coaches out there who are doing it," he said, according to the Sun.
"I love football," he added, according to the Sun. "It's what I am. I miss it."
Last week, Ohio State athletic director Gene Smith said no deal had been struck with Meyer. Other Ohio State athletic officials also have denied the reports.
The 47-year-old Meyer is an Ohio native. He started his coaching career as a graduate assistant coach for the Buckeyes in 1986.
He resigned as Florida's coach on Dec. 8, 2010, saying he wanted to spend more time with his family. Meyer won two national championships at Florida and 104 games over 10 years with the Gators, Utah and Bowling Green.
Ohio State promoted Luke Fickell to interim coach nearly six months ago when Jim Tressel resigned amid an investigation into players trading memorabilia for tattoos in violation of NCAA rules.
Information from The Associated Press and ESPN.com college football writers Adam Rittenberg and Chris Low was used in this report.