According to Dow Jones, an official from the company said the deal was still being negotiated.
Once finalised, it will be signed within four weeks.
The Emirates logo will then appear on the La Liga club's shirts for between four and six years.
In an interview with an unnamed source, they said the sponsorship would be exclusive.
It will not effect Emirates' deals with other teams, including as shirt sponsor of Arsenal FC in the English Premier League, Paris Saint-Germain in the French Ligue 1 and AC Milan in the Italian Serie A.
At a press conference earlier this year, His Highness Sheikh Ahmed bin Saeed Al Maktoum, the chairman and chief executive of Emirates Airline, said total sponsorship spending by Emirates this year would be about Dh1bn.