The two began dating earlier this year and are now considering moving into an apartment together in New York.
According to Star magazine, they have already started house hunting. An article in the magazine stated, "They’re discussing moving in together in NYC. I know that they have already started looking at places to buy in Soho and the West Village."
Scarlett Johansson is best known for her role in Lost in Translation. Hartnett is known for the films Black Hawk Down and Pearl Harbor.