The pair - who co-starred in TV movie 'Northern Lights', with rumours they were romantically involved first circulating in March - were spotted at a golf course in Valencia, California.
They seemed relaxed and at ease with each other, and spent the day riding around in a golf cart, hugging and chatting.
On Saturday (22.08.09), the couple were again seen at a Kings Of Leon concert in Los Angeles, where they chatted intimately.
Despite initially claiming reports of her infidelity were untrue, LeAnn, 26, and her husband-of-seven-years Dean Sheremet split last month.
Neither has referred to any alleged affair since their break-up, instead insisting they simply grew apart.
A source said at the time: "They were so young when they got married, she was 19, he was 21. Maybe they just grew up and they weren't in the same place anymore. I don't think that's unusual considering how young they were when they got married, and the business they're in."
Eddie has also split from his wife Brandi Glanville, with who he has two children.
Brandi confirmed: "Eddie and I have decided to take some time apart. I want to do what is best for our children. Eddie and LeAnn deserve each other."
Meanwhile, LeAnn's representative has responded to reports the singer was questioned by Los Angeles police regarding an alleged hit and run which took place in Brentwood, Los Angeles, last week.
The spokesperson said: "There was a routine police investigation into this incident, and a police report was filed. We are confident that this matter will be resolved shortly and LeAnn will be cleared."