Patrick made the comments Tuesday while appearing as a guest on the Jenny McCarthy Show on SiriusXM.
Rodgers and Patrick confirmed that they were dating in January. The Green Bay Packers quarterback attended the Daytona 500 in February as Patrick's guest. Rodgers and actress Olivia Munn dated for three years before announcing their split in April 2017.
Patrick and fellow driver Ricky Stenhouse Jr. ended their five-year relationship in December. Patrick said that she met Rodgers at the 2012 ESPYS. They kept in touch via email.
"We remember meeting each other," Patrick said on the radio show. "It was quick. I got his email address. I remember thinking to myself back then 'Oh, on the down low. Not a phone number just an email address. Which is whatever. I don't know."
"We kept in touch just a little bit. There were some years I don't think we talked to each other. And then some every now and again. It wasn't until obviously recently that we actually had phone numbers. We referred to each other as 'Chicago' and 'Green Bay.' It was very cute."
Patrick was born in Wisconsin but grew up as a Chicago Bears fan.
"It's like the Capulets and the Montagues," Patrick said. "I've made like slight mentions and he's like 'Don't even go there. We aren't going to talk about that.' I agree. No one is going to wreck me as an athlete. That's up to me. It's up to me to control my environment and my own emotions and do what I need to do to do my job well. Anything other than that should be good."
"Thats what I say I'm here to add, not take away. I'm here to make you happy."
Patrick straps in for her final race in the Indianapolis 500 Sunday at Indianapolis Motor Speedway. She will start in seventh place for the IndyCar series event.
Rodgers and the Packers reported to organized team activities on Monday and have mandatory minicamp from June 12 to June 14. The two-time NFL MVP played just seven games last season, while hampered by a broken collarbone.
Patrick will be the first woman to host the ESPYS when she takes the stage on July 18 at Microsoft Theater in Los Angeles, Calif.