Reports said the company is due to announce plans for a stock market listing as early as Tuesday, taking advantage of a housing market pumped up by state stimulus schemes.
Bosses could be in line for a windfall of up to £100 million, the Sunday Times said, with a flotation likely to value the chain at between £400 million and £500 million.
Private equity group BC Partners bought Foxtons for about £375 million at the peak of the market in May 2007 from founder Jon Hunt , just months before the credit crunch sent house prices plunging. It has already appointed investment banks to advise on a flotation.
The company was taken over by its lenders in 2010 in a deal which slashed its debt, before the private equity firm regained control last year.
A sale would mark a substantial turnaround in fortunes for BC Partners, which also owns mobile phone retailer Phones4U. It has reportedly described its purchase of Foxtons as a ''mistake''.
Foxtons, which has a distinctive fleet of Minis, has recovered as wealthy foreign buyers fuel London house prices.
The market has also been given a boost in recent months by Government schemes such as Help to Buy, which offers loans to allow people to buy new-build homes with a deposit of just 5%.
Chief executive Michael Brown and fellow management reportedly own 20% of the company, setting them up for a multi-million pound windfall from the flotation.
The UK's biggest estate agency chain Countrywide also rejoined the stock market earlier this year, valued at more than £800 million. The group, which has almost 1,000 branches, trades through brands including Bairstow Eves, Gascoigne-Pees and Hamptons International.
London-based BC Partners lined up Credit Suisse, Numis Securities and Canaccord Genuity to advise on the stock market flotation.
BC Partners declined to comment.