Matt Damon has reportedly proposed to his bartender girlfriend Luciana Barroso after a one-year courtship.

"It's very hush-hush," Internet Media Database quoted a source as saying.

The couple are currently house-hunting in Barroso's hometown of Miami, Florida, and looking at schools for the beauty's six-year-old daughter Alexa.

The "Bourne Supremacy" star, 34, began dating the aspiring interior designer in April 2004. He even brought her to Europe during filming on "Ocean's Twelve" last summer.

When asked to confirm or deny the reports, Damon's spokesperson had no comment.