The 23-year-old actress has been seen getting close to the TV actor at the Hollywood restaurant Bagatelle LA, reported New York Post online.
Rumer joined Blair as he dined with nine friends and the two stars sat next to each other and held hands throughout the evening.
"She sipped on bourbon, while Jason draped his arm around her the whole evening. The two were holding hands, flirting and canoodling," a source said.
After the meal, the pair went to Hollywood's Sayers Club, where the "Sorority Row" star performed several songs.
