Miller, 30, has been dating actor Tom Sturridge, 26, for about a year. She previously had a high-profile relationship with British actor Jude Law, who admitted he cheated on her with his children's nanny.
"Friends are really happy with her relationship with Tom," an insider told the celebrity news Web site. "He's younger, yes, but he's mature and he's a good guy."
The source said the couple "don't have plans right away to marry, if at all."
When Miller is to give birth and what the baby's gender is were not immediately reported.
Miller, who was born in New York and raised in London, is known for her work in "Layer Cake," "Alfie," "Factory Girl," "The Edge of Love" and "G.I. Joe: The Rise of Cobra." She also was a victim of the 2011 News of the World phone-hacking scandal in Britain.
Sturridge appeared in "The Boat That Rocked" and will soon be seen in "On the Road."
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