The duo were spotted touring homes on the west side of Los Angeles on Tuesday. Shookus wore ripped black jeans and a sheer top, while Affleck opted for a black T-shirt and maroon pants.
“Ben is looking to buy a family friendly house,” a real estate source tells PEOPLE. “Lindsay shared her opinions, but it was clear that they are not buying a house together.”
One home they toured in Santa Monica runs $18.5 million and has 8 bedrooms, 10 baths, 9,422 square feet, 1,000 bottle wine cellar, a movie theater and a gym, according to its listing.
Another home they toured in the Pacific Palisades is listed for $11.9 million and has 5 bedrooms, 6 baths and a 6-car showroom garage.
Affleck, 45, and Shookus, 37, a producer for Saturday Night Live, went public with their relationship in July.
The Justice League star had been living in a rental since he moved out of the family estate he used to share with his ex-wife Jennifer Garner and their kids, Violet, 11, Seraphina, 8, and Samuel, 5. Affleck was living in the guesthouse during their separation, and moved out a month after they filed for divorce in May.
Another source says that Affleck never loved his rental and always planned on buying a house.
All the houses they toured are fairly close to Garner’s family home, which a source previously told PEOPLE was important for Affleck, who wants to be nearby his kids.