Is Sean Penn Moving to Adopt Charlize Theron's Son?
updated 01/23/2015 AT 03:10 PM EST
•originally published 01/23/2015 AT 11:05 AM EST
Despite reports the actor has filed papers requesting to adopt his actress girlfriend's 3-year-old son Jackson, PEOPLE has since learned that Penn is not currently planning to adopt the boy.
Penn, 54, and Theron, 39, have been dating for over a year. "Charlize and Sean are very serious," a source close to Theron tells PEOPLE. "Charlize says this is it. Jackson already calls Sean 'Daddy.' "
Theron adopted Jackson in early 2012, when he was 4 months old. Jackson is her only child.
Penn has a daughter, Dylan, 23, and son, Hopper, 21, from his marriage to Robin Wright.
The couple have been quiet through persistent marriage speculation over the past year, but friends have said they are a great match.
"[Charlize] likes guys with more substance. She finds Sean very charming and he makes her laugh," a source told PEOPLE last year. "She definitely has him wrapped around her finger."