"[She's] told people she's going to name the baby Ace," an insider said, adding Simpson and her fiance, Eric Johnson, have not revealed why they like that name in particular.
The couple are also parents of a 10-month-old daughter named Maxwell.
The new baby's gender has not been disclosed yet.
Johnson is a former San Francisco 49ers and New Orleans Saints tight end.
Swim Week Miami Beach 2014 [PHOTOS]