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The actress met Getty while filming GI Joe in May, according to The Mirror. Miller was still in a relationship with Rhys Ifans at that time.
Getty is married to June Catherine and has four children. His wife is allegedly speaking to divorce lawyers today.
"They began meeting in Prague and that was when the chemistry started and he began wooing her," said a source.
"She had a boyfriend and it didn't immediately turn physical but there was something there. This behaviour is typical Sienna. She loves the power of being able to take a man off another woman."
Miller apparently spent the last week living with the Brothers And Sisters star at his Hollywood home.
