(Adds details, background)
MADRID, Nov 24 (Reuters) - Spanish construction firm FCC's largest shareholder is in exclusive talks to sell Mexican billionaire Carlos Slim its rights to buy shares through a planned 1 billion euro ($1.24 billion) capital increase.
A sale of the rights would hand Slim the potential to take a roughly 25 percent stake in the Spanish firm, diluting the shareholding of the family that founded it.
Esther Koplowitz, whose father set up FCC and who currently holds a stake of just over 50 percent, had been in talks to sell the rights to financier George Soros, but negotiations collapsed.
Instead, FCC said in a statement to the stock exchange on Monday that Koplowitz's B-1998 firm -- which is struggling with its own debt problems and cannot participate in the capital increase -- was now in talks with Slim's Inmobiliaria Carso.
Shareholders in FCC last week approved the rights issue aimed at raising funds to help FCC cut back a costly 6.4 billion euro debt burden.
A source close to the process told Reuters on Monday that the final details of the capital increase, including its price, would not be set until a deal was struck by Koplowitz, and an investor brought in to take up her rights.
"Placing one billion euros in the market is not the same as having 500 million euros already assured," the source said.
FCC, like fellow Spanish builders, has sold non-core assets, laid off staff and restructured borrowings to pare down its balance sheet, following a 2008 property bust which pummelled earnings and left many construction companies with huge debts.
Without a deal between Koplowitz's investment vehicle and Slim there could be delays to the company's debt refinancing deal, which includes a haircut of 135 million euros for creditor banks. (1 US dollar = 0.8069 euro) (Reporting by Carlos Ruano and Sarah Morris; Editing by Julien Toyer and Clara Ferreira Marques)