According to editors at New York Post's Page Six, the rapper and reality TV star are quietly in the process of buying a place in the city's 18-storey luxury beachfront tower Faena House, which is home to Goldman Sachs chairman Lloyd Blankfein, hedge-fund billionaire Kenneth C. Griffin and Faena co-developer, businessman Len Blavatnik.
They reportedly signed a contract to buy the property from Blavatnik's brother Alex, who had originally listed it for $15.5 million (£12.3 million). The apartment is 4,700 square feet and boasts four bedrooms, five and a half bathrooms and a wraparound terrace. The building also has a private gym, spa, pool, concierge and underground parking.
"Kim and Kanye have been spotted viewing the property in the last month, and they are now in contract to buy it for $14 million. The sale is expected to close in January," a source told the publication.
They have long-running connections with Miami Beach, with the Kardashian sisters opening a DASH boutique store in the city and Kim starring in "Keeping Up with the Kardashians" spin-off "Kourtney and Kim Take Miami", which ran for three seasons until 2013. Kanye is also a regular at the annual Art Basel Miami Beach, and is said to like Faena's links to the artistic and cultural community.
The couple, who has three children; North, five, Saint, three and Chicago, 11 months, is mostly based in their mansion in Hidden Hills, California. In November, they hired private firefighters to save their home during the California wildfires.
Representatives for Kim and Kanye didn't comment on the report.