According to the source the two "were making out" while soaking in the sun on Ditch Plains Beach, reported Us Weekly.
Johansson, 32, and Jost were accompanied by his brother and sister-in-law.
The "Ghost in the Shell" star was first spotted getting close with Jost at a May 20 SNL after-party. The duo also enjoyed a date at NYC's The East Pole in June.