A source tells Us Weekly the 53-year-old actor and 38-year-old actress "want to get married very soon."
The couple will reportedly marry in Theron's home country of South Africa this summer, where they also intend to adopt a child. Theron is already mother to 2-year-old son Jackson, whom she adopted from South Africa in 2012. A different source tells the magazine the actress "always intended to have another child."
Penn and Theron are in the country to shoot new drama The Last Face. Penn will direct the feature, with Theron and Javier Bardem to star. The two portray doctors involved in humanitarian efforts who must choose between love and dedication to work.
The marriage would be Penn's third; he was married to Madonna from 1985 to 1989, and to Robin Wright from 1996 to 2010. He and Wright have two children, 23-year-old daughter Dylan Frances and 20-year-old son Hopper Jack. Theron was previously in a relationship with Stuart Townsend from 2001 to 2009.
Penn and Theron made their first public appearance as a couple in January.