Matt Damon and his girlfriend, Luciana Barroso, are engaged, Us Weekly reported Monday.

A publicist for the "Bourne Identity" actor told the magazine that after dating for two years, Damon popped the question "shortly before Labor Day." Damon's publicist, Jennifer Allen, didn't immediately return a call from The Associated Press late Monday. The couple haven't set a wedding date, Us Weekly said. It would be Damon's first marriage. Barroso has a daughter, Alexa, from a previous relationship.