It is the first time the Gulf carrier has ordered Rolls-Royce engines for its superjumbo fleet, the rest of which is powered by Engine Alliance, a joint venture of General Electric and Pratt & Whitney. Airbus and Emirates declined to comment on the deal, earlier reported by France's La Tribune newspaper.
A spokeswoman for Rolls-Royce said the company did not comment on market rumours.
Emirates is due to make what it has described as a major business announcement in London on Friday, but has declined to say what it will be about.
The airline's president Tim Clark said in March he was considering Rolls-Royce engines for the 50 engines yet to be delivered.
The expected deal comes as Airbus ponders a possible upgrade of the A380 with newer Rolls-Royce engines to improve its efficiency in response to persistent requests from Emirates, the largest customer. Many see that as a make or break decision for the double-deck jetliner after a period of slow sales.
Both Airbus and Boeing face increasing pressure to boost the sales performance of their largest passenger planes, the A380 and the Boeing 747-8 as some airlines abandon the jumbo jet category for smaller planes.