Carlyle is understood to be working with investment bank William Blair on a potential sale.
An auction process, which is is expected to attract interest from private equity and strategic buyers, is likely to kick off in the first quarter of 2017, one of the people said.
The carpetmaker is expected to fetch more than £200 million, another person said.
An exit would mark the end of five years of ownership for Carlyle, which acquired the 233-year old carpet supplier out of administration in 2011 for £38 million, Private Equity News reported at the time.
Brintons Carpets, which was awarded a Royal Warrant by the Queen in 1958, has provided carpets for venues including Indira Gandhi International Airport in Delhi, the Queen Mary 2 and Buckingham Palace.
Its earnings before interest, taxes, depreciation and amortisation doubled to £8 million for the financial year to September 26, 2015, up from £4.1 million in 2014, according to filings with Companies House.
Earnings were boosted by a reduction in manufacturing costs and a 10.9% increase in revenue growth, the filings said.
Brintons also completed the acquisition of Poland-based FD Agnella, a manufacturer and supplier of carpets, in July 2015 to add to manufacturing operations in India and Portugal. Brintons Group also has sales offices in the US and Australia.