The twice-married Hollywood actress has been dating the French-Canadian model since 2005, and she gave birth to the couple's first child, daughter Nahla, now two, in 2008.
The couple reportedly worked out a "very short-term custody arrangement" for their daughter three weeks ago, according to TMZ.com.
The Monster's Ball star was previously married to former baseball player David Justice, but the three-year union ended in 1993. Berry divorced her second husband, musician Eric Benet, in 2005.
The Oscar-winner previously stated she had "no plans" to marry Aubry, insisting their relationship "worked" without an official commitment.