According to the New York Post, the Tree of Life star was spotted enjoying a romantic break at the Beverly Hills Hotel Peninsula with Stacy Koplin.
"She came up to the roof with wet hair, he looked totally frazzled," an onlooker told the newspaper about the potential couple's open-air holiday breakfast. "They were in deep conversation the entire time."
Penn and Johansson began officially dating in March, only months after Johansson's split from husband Ryan Reynolds. However Penn allegedly ended the relationship last month.
Reports suggest that Penn broke it off with Johansson because he is still not ready for a serious relationship, following the end of his 14-year marriage to Robin Wright last year.
Watch Sean Penn in the trailer for his new film The Tree of Life below: