Private equity firm Najafi Companies is reportedly in discussions to buy Borders in America.
The Wall Street Journal reports "people familiar with the matter" said the firm, which usually makes investments of $1bn or less, is in competition with another private equity company Gores Group to buy the bookstore chain.
Both firms are thought to want to keep the chain operating as a “going concern".
Najafi has also recently bought the French Direct Group Business of CD and DVD clubs from Bertelsmann AG, Europe’s biggest media company.
Borders had 642 stores before closing 237 of them after filing for court protection in February.
Under Chapter 11 of the bankruptcy code, the company would hold an auction to sell itself, and find the best deal to repay its creditors.
Last week it was announced that Borders stores in Australia would close in a week as the remaining bookshops were given their closing notices after no buyer could be found for them.
On Tuesday, The Bookseller reported that more than 230 former Borders employees in the UK who lost their jobs when the company closed down in December 2009 had been awarded the maximum 90 days' pay by an employment tribunal.