The footwear company has received several offers in the past month and appointed investment bank NM Rothschild to evaluate them.
One party is in detailed talks with the iconic shoe brand, which is valued at an estimated£180 million.
Lion Capital owns a 51 per cent stake in the business at£101 million and Mellon owns the remaining 49 per cent.
Jimmy Choo pumps, sandals and boots were glamorised by Sarah Jessica-Parker in the hit series Sex and the City, and loyal customers to the brand include Gwyneth Paltrow and Nicole Kidman. A pair of boots can fetch up to£1,200.