TA Associates snapped up 60% of the brand, known for its floral print products, in 2010 in a deal thought to value it at around £100m.
TA is now said to be mulling whether to put the company on the market.
A spokesman for Cath Kidston declined to comment on the sale claim but confirmed that a review of its future was under way and it had appointed advisers at UBS to help assess its options.
The business has just opened a new flagship store next to the Ritz in central London and last month launched an outlet in Shanghai.
The spokesman said: "Cath Kidston is growing rapidly and has exciting plans to capitalise on the international appeal of its brand.
"In these circumstances, it is prudent that the company and its owners should carefully assess the options available to take the company through the next stage in its evolution and UBS has been appointed to help."
TA Associates is expected to seek more than £250m for the business.
It is unclear if Ms Kidston will sell any of her 23% stake in the company.
Ms Kidston, 54, founded her first store in 1993 in west London. The brand now has 59 shops and concessions in the UK and Ireland as well as 54 across Spain, Japan, South Korea, Thailand, Taiwan, Hong Kong and China. Annual sales are about £105m.