As per a report in French outlet RMC Sport, the 27-year-old has already undergone his medical at the West London club and is set to pen a loan deal at the newly-promoted Premier League club.
The French shot-stopper only made nine appearances for Los Blancos last season, acting as an understudy to Thibaut Courtois throughout the campaign.
Areola – who spent the 2015/16 in Spanish football with Villarreal – made four appearances in La Liga, three in the Copa del Rey and two in European competition.
A separate report from Sky Sports claimed that Ligue 1 club Rennes were also in the running for Areola, with their number one Edouard Mendy set to leave the club for Chelsea.
Andriy Lunin is now the only other goalkeeper on Madrid’s books, after the exits of Keylor Navas and Luca Zidane in the past year.