Spears, 16, and Aldridge, 18, are expecting their first child this summer.
The actress is best known for her role on TV's "Zoey 101," and for being the younger sister of pop star Britney Spears.
"She's got an engagement ring," a source close to the family told People.com. "She's been showing it off, talking about it."
The couple have not announced a wedding date, the report said.