The 161-year-old business, which has been the subject of takeover interest in the past year, could be valued at between £200 million and £300 million in a stock market flotation, the Sunday Times said.
Executive chairman Don McCarthy and his family hold a 20% stake with a further 49% in the hands of representatives of failed Icelandic banks, who took control of the shares when previous owner Baugur went bust.
The retail business, which generates sales of £1.2 billion a year, has 61 UK and Ireland stores covering nearly five million square feet of selling space. It employs 7,300 people as well as 12,000 concession staff.
House of Fraser, o ne of Britain's best known retailers, is believed to have held takeover talks in recent months with Sports Direct tycoon Mike Ashley and the Qatari royal family but is now considering a return to public ownership.
In 2006, it was snapped up by a group of investors led by Icelandic tycoon Jon Asgeir Johannesson's Baugur Group in a £350 million deal. Other chains in the Baugur portfolio included toy store Hamleys and frozen foods chain Iceland.
The chain first listed on the stock market in 1948 and remained a public company until it was bought by Mohamed al-Fayed in 1985.