Maybe Scarlett Johansson and Sean Penn are dating after all. The two mega-movie stars jetted off to Mexico for a whirlwind trip on Tuesday, PEOPLE reported.

Johansson and Penn departed on a private jet from Van Nuys airport Tuesday morning and were spotted enjoying a lobster dinner Tuesday night in Cabo San Lucas, Mexico. The pair returned to Los Angeles early Wednesday morning where Johansson is filming 'We Bought a Zoo' with Matt Damon.

The twosome was also seen sharing an intimate lunch earlier this week at Los Angeles Cuban restaurant, Versailles. At the lunch, Johansson was photographed with her leg in Penn's lap.

The 'Avengers' actress and 'Milk' actor were first seen together in early February when they were nearly inseparable at a party celebrating 'Black Swan.' "They were flirting with each other all night, pretty much ignoring everyone else," a source told PEOPLE at the time.