The 161-year-old business, which has been the subject of takeover interest in the past year, could be valued at between £200m and £300m in a stock market flotation.
Executive chairman Don McCarthy and his family hold a 20 per cent stake with a further 49 per cent 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 £1.2bn a year, has 61 UK and Ireland stores – including Hull, Grimsby, Leeds, Sheffield, Skipton and Huddersfield – covering nearly five million square feet of selling space.
It employs 7,300 people as well as 12,000 concession staff.
House of Fraser, one 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 said to be considering a return to public ownership.
A spokesman for the premium chain told the Yorkshire Post: “No comment.”
In 2006, House of Fraser was snapped up by a group of investors led by Icelandic tycoon Jon Asgeir Johannesson’s Baugur Group in a £350m deal.
Other chains in the Baugur portfolio included toy store Hamleys and frozen foods chain Iceland.
A Sunday newspaper report said the float plans were being led by Mr McCarthy but are at an early stage and may come to nothing.
Other big shareholders include Scottish tycoon Tom Hunter and Lloyds Banking Group, which inherited its stake after Halifax Bank of Scotland helped finance Baugur’s takeover deal.
“There’s been speculation around House of Fraser and changes of ownership since the Icelandic situation blew up,” said a source.
“The change of shareholder structure is something the business will look to resolve at some point.”
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.
House of Fraser is moving with the times and its decision to invest in its online platform is paying off with online sales increasing 53 per cent last year.
The chain reported a 4.2 per cent hike in earnings before interest, debt, tax and amortisation of £61.1m in the year ending January 26.