The G.I. Joe actress has put a deposit down on her "dream home" and asked her boyfriend of four-months to move in with her, according to The Mirror.
"This is her dream home and she really can't wait to move in," a source said. "People may think that four months isn't a very long time for a couple to be together, but Sienna wears her heart on her sleeve."
Miller was first romantically linked to Sturridge, who is best known for his role in The Boat That Rocked, back in February.
The pair were pictured together weeks after Miller ended her romance with former fiancé Jude Law.
The Sherlock Holmes star moved to an £8m bachelor pad in Highbury after the split.