According to The Blast, the couple have privately been house hunting for a home in Los Angeles. They even revealed their intentions to find a home at an open house earlier this month.
At the time, they viewed a 3,400 sq foot farmhouse in Studio City with 5-beds and 6-baths. The property, which is currently listed at $2,399,999, included wide plank oak hardwood floors, Thermador kitchen appliances in a huge chef's kitchen and large windows.
Readers know Culkin, 38, and Song, 31, have been dating since July 2017.
In December of that year, Radar exclusively reported the two had eloped in Paris during Thanksgiving weekend, and "didn't tell a single soul" about their nuptials.
Due to complications over a marriage license, Radar learned they might have to get married again in America.
"Brenda wants to make things official with a proper wedding, and Mac would do anything to make her happy, so the plans are already in motion," shared an insider.
Culkin previously dated Mila Kunis, who admitted they had "a horrible, horrible breakup," adding that she had "f***ed up."