The London-based company, which has 40 branches in the capital and two outside, as well as a new luxury Alexander Hall office in the West End, is believed to be seeking to take advantage of the housing market recovery.
It is rumoured to be planning the opening of a raft of new branches outside London.
Foxtons is currently majority owned by private equity firm BC Partners, while its executive directors are reported to own 20% of the equity.
The proceeds from the initial public offering (IPO) will be used to clear all of its debts, the company said in stock market statement.
Foxtons said it was well placed to “benefit from any future recovery in the residential property sales market”.
First-half revenue at the group rose 10.5% to £62.6m, while adjusted earnings before interest, tax, depreciation and amortization rose 14.3% to £19.4m.
Foxtons founder Jon Hunt has already made his fortune from the business. He set it up in 1981, then sold it to BC partners for around £375m in 2007, just months before the UK housing market nosedived.