Is Sean Penn ready to propose to Charlize Theron?

Los Angeles - Sean Penn is reportedly planning to propose to Charlize Theron.

Friends close to the couple, who began dating at the end of last year and flew to Hawaii to celebrate New Year's Eve together in December, predict the Milk actor and the South African actress will get engaged in the very near future, but insist they haven't started making wedding plans just yet.

An insider told PEOPLE.com that they "wouldn't be surprised" by a proposal, adding: "But she's not engaged - yet."

The duo, who went public with their relationship at Sean's third annual Help Haiti Home gala in January, were "inseparable" when they flew to Cabo San Lucas in Mexico for Valentine's Day weekend in February.

An eyewitness said at the time: "They held hands everywhere they went."

The 53-year-old actor is set to direct his Oscar-winning girlfriend and Javier Bardem in The Last Face, which is expected to begin filming in Africa later this year.

A source previously claimed that the couple, who recently moved in together in Los Angeles, have also talked about adopting a child together.

Sean already has two children, Dylan, 23, and Hopper, 20, with his ex-wife Robin Wright, while Charlize, 38, has a two-year-old son Jackson, whom she adopted in March 2012.