Simpson, 32, is already a mother to 10-month-old daughter Maxwell, reported Us magazine.
"She's told people she's going to name the baby Ace!" a source said.
Last year, Simpson said that Maxwell's unique moniker came about as a tribute to both her family and her NFL player fiance.
Maxwell is Johnson's middle name as well as his grandmother's surname, and Drew is Simpson's mother Tina's maiden name.