The Victoria's Secret model - who replaced Megan Fox in the Transformers movie franchise - hooked up with Statham in April this year and is planning to live with The Expendables star at his new Los Angeles home.
"They seem very happy together. Rosie's on the make and being with a big star like Jason is doing her career no harm at all," a source told Britain's Daily Mail newspaper.
"She has been excitedly telling all her friends that they are going to be moving in together."
However, Rosie has been using her Transformers costar Shia LaBeouf to make Jason jealous!
"Rosie jokes about how sexy Shia is because she knows it winds Jason up. Jason wants to make sure he holds on to Rosie, and moving in is a sign of his commitment to her," said the source.