Founder Alex Chesterman could net a fortune of more than £100 million from the share sale after starting the company six years ago, according to the Sunday Times.
It comes amid City speculation about a raft of potential flotations amid burgeoning signs of economic optimism, including an improving property market buoyed by Government initiatives such as the Help to Buy scheme.
Last month estate agency chain Foxtons confirmed it was planning to cash in on surging London house prices with a public offering of shares that is expected to earn directors a windfall of up to £100 million.
A Zoopla spokesman said: "As one of the fastest growing online businesses in the UK, our focus is on continuing to develop our brands and business in a sustainable way.
"We work with various advisers and have recently engaged Credit Suisse to help us explore further strategic opportunities as we continue to grow."
According to the Sunday Times, a float was considered the most likely option amid estimates valuing the fast-expanding company at £1 to £1.3 billion.
It would represent his second windfall after Amazon's £200 million takeover of film rental firm Lovefilm two years ago, the Sunday Times reported.
Sources close to Zoopla stressed that a stock market float was just one of a number of options that would be considered.
It was reported that Daily Mail & General Trust would retain a majority stake if the company did decide to go public.
Zoopla describes itself as one of the fastest-growing websites in the UK with more than 20 million visits per month.
The site was originally set up to provide an instant valuation for any property in the UK but has since bulked up via a merger with Digital Property Group, home of the Prime Location and Findaproperty.
Last week it bought another set of property websites from publisher Trinity Mirror.
Mr Chesterman has reported to have said he would leave "no stone unturned" until Zoopla had overtaken rivals Rightmove as the leading property website.
Elsewhere, there was renewed speculation about a stock market flotation for Legoland and Madame Tussauds owner Merlin Entertainments.
According to the Sunday Telegraph it was planning to offer more than 10% of shares to retail investors as it geared up for a £3 billion-plus listing before Christmas. A spokeswoman declined to comment.