Tehan, 31, who has a 1-year-old daughter, was reportedly seen several times in the convenience store this month and last, with Tre B. Hutcherson, 42, of Dayton, according to the Dayton Daily News.
Surveillance video captured the pair together two weeks before her disappearance, according to CBS News' The Early Show.
Her family members say they don't know Hutcherson or why Tiffany Tehan would be with him.
On Saturday, Tehan set out for garage and consignment sales in the area. Xenia is about 20 miles west of Dayton.
When she didn't return home, her husband, David Tehan, called police around 9 p.m to report her missing.
Her SUV was found Sunday morning at a park in the Dayton suburb of Kettering. It had a flat tire and the keys were locked inside.
"Tiffany, we love you. We care for you, and if you are able to contact us, please do so, her father Chuck Tabor told The Early Show. "We'd like to... make sure that you know that you can come home, and we want to do everything we can to find you."
It's believed that she was at The Greene shopping center in Beavercreek at around 11 a.m., according to the Associated Press.
Xenia police said Monday they have received more than two dozen calls regarding the missing mom.
Police say they are checking cell phone, credit card and other records. Hutchinson owns a "1999 red Volkswagen Beetle with an Ohio license plate No. EVQ9018," police told the Dayton Daily News.
Tiffany Tehan's family has created a Web site and is asking for the public's help in finding her. They are offering a $5,000 reward.