The couple began dating last summer.
"They broke up shortly before her birthday (last month), then got back together," an insider told UsMagazine.com.
"Joe wasn't that into it," a second source told the celebrity news Web site about the short-lived relationship.
Greene is best known for her work in the "Twilight" film franchise. She will soon be seen in the 1980s movie "Skateland," as well.