Showbiz
Rex Features
The 26-year-old has been dating Warren since he worked as a director's assistant on the set of her 2004 movie Fantastic Four.
The couple broke up in July, but were believed to have reunited a few weeks later.
Alba's spokesperson Brad Cafarelli said: "I confirm that Jessica and Cash are expecting a baby in late spring, early summer."
The actress recently revealed that she wants to develop a "tough girl" image so she is regarded as more than a pretty face.
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