According to a source, the 27-year-old's relationship with DiCaprio, 40, is steaming up as they are spending a lot of time together in his home, reports femalefirst.co.uk.
"It's like she's practically moved in," The Sun newspaper quoted the source as saying.
"Leo has been sweet and cordoned off little areas for her in the home that are just for her, like a smoke room," the source added.
The couple were first rumoured to be dating shortly before Christmas, but their relationship has quickly gone from strength to strength and Rihanna has already promised to take DiCaprio back to Barbados next month, where he will be a guest at her cousin's wedding.
The pair will also use their trip to the island to enjoy a romantic getaway together, planning to escape for some alone time on a nearby yacht.
The source said: "Afterwards Rihanna and Leo are going to spend a few days by themselves on a yacht."