House of Fraser in takeover link
The retailer, which has 61 stores in the UK and Ireland, is said to be looking for a price tag of at least £450 million, the Financial Times said.
At the same time it is believed to be continuing with preparations for a flotation on the London Stock Exchange early next year.
Family-controlled Galeries Lafayette, which has 65 stores, has exclusivity on the talks with House of Fraser until the end of January.
It is looking at overseas expansion as a way of compensating for a slow-growing domestic market in France.
House of Fraser, which generates sales of £1.2 million a year and employs 7,300 people as well as 12,000 concession staff, has been the subject of takeover speculation in the past year.
It is believed to have held informal takeover talks with Sports Direct tycoon Mike Ashley and the Qatari royal family before setting its sights on a return to public ownership.
The chain, which is 161 years old, first listed on the stock market in 1948 and remained a public company until it was bought by Mohamed al-Fayed in 1985.
It was listed again in 1994 before being snapped up in 2006 by a group of investors led by Icelandic tycoon Jon Asgeir Johannesson's Baugur Group in a £ 350 million deal.