Selena was wearing a low-cut gray top and jean shorts during the outing.
For a photo of Selena and David walking together without anyone else around, click here.
The night before, Selena was enjoying the single life while partying with gal pals at the Chateau Marmont.
David, who is 23, can be seen in this summer's Adam Sandler comedy, Grown Ups 2.
So might David and Selena be a new couple? We totally approve, especially since David is totally cute — not to mention that he doesn't own a monkey, or threaten photographers, or constantly walk around shirtless, or... need we say more?
We'll have to wait and see if David is ready to come and get it.