A source told In Touch that the couple have "moved in together in a big house near Runyan Canyon".
Frances Bean and Silva changed their Facebook relationship statuses to "engaged", according to the reports.
The 19-year-old daughter of Courtney Love and the late Kurt Cobain wrote on her Facebook wall: "Getting to spend the rest of my life loving my best friend makes me the luckiest woman in the world."
Frances Bean allegedly turned down the role of Bella in Twilight.
Love, who lost custody of Frances Bean, has said that her daughter is not interested in becoming famous.
"She was offered the part of Bella in the Twilight movies, and Tim Burton wanted her for Alice in Wonderland," Love said. "But she wants to go to college - she's very good at graphic novels... Frances will be fine."
Bean made her music debut last year, appearing on Amanda Palmer's album.
Watch the video for Hole's 'Celebrity Skin' below: