The 35-year-old actress, who separated from her husband of six years Roberto Zincone in November last year, was first spotted going out for a dinner with Egglesfield, 41, at Sugarfish Sushi in Beverly Hills, California early this month, reported Ace Showbiz.
"They're getting to know each other. They're taking it slow," a source said.
Roberto filed for divorce from Akerman, citing "irreconcilable differences." They have a one-year-old son named Sebastian.