MADRID/MILAN/ROME (Reuters) - Spain's ACS and Italy's Atlantia said they are in talks over their competing bids for Spanish toll road company Abertis and a source said they could decide to break up the company rather than press on with a costly takeover battle.

"If a deal is reached, Atlantia would likely withdraw its offer for the Spanish company and sign an agreement with ACS on how to divide Abertis's assets," the source close to the matter said.

Atlantia would be interested in the Italian, French and part of the Latin American assets of the Spanish toll-road operator, the source said.

ACS, in turn, would get a portion of Abertis's activities in Latin America and all its Spanish assets, the source said, adding this would soothe the concern of some Spanish ministers over Atlantia's clout in the country.

Isidro Faine, the head of Criteria Caixa, the investment arm of a politically connected banking foundation, brought Atlantia and ACS to the negotiating table, the source said.

"The talks aim at avoiding a bidding war that would load the winner with a mountain of debt," the source said. "If the two companies are reasonable, a deal could eventually be reached."

The long-running battle for Abertis pits the Benetton family, which controls Italian motorway and airport operator Atlantia, against Spanish businessman and Real Madrid president Florentino Perez, the leading investor in ACS.

ACS is bidding through its German arm, Hochtief.

Atlantia and ACS, in separate statements to the Spanish market regulator, confirmed on Thursday the existence of preliminary talks, but said there was no agreement so far.

The two groups and Abertis declined to comment on details of the potential asset break-up.

An official at Criteria Caixa, which holds a 21.55 percent stake in Abertis, said the investment vehicle was not aware of talks between the two suitors.

ACS, ATLANTIA SHARES RISE

Atlantia and ACS have spent weeks in talks on how to break up Abertis between them and avoid an expensive bidding war, Spanish financial newspaper Expansion reported, without citing sources.

At Wednesday's closing prices, Hochtief's offer values Abertis at around 17.9 billion euros, taking into account a reduced offer with Abertis paying a dividend; while Atlantia's offer values Abertis at around 16.7 billion euros (14.90 billion pounds). Both values include Abertis' treasury shares.

Abertis shares were trading 3.7 percent lower at 1355 GMT, while ACS led gains on the Spanish blue chip index, rising 8.6 percent. Atlantia rose 4.3 percent.

Investors and analysts reacted positively to the news, saying it was neither in Atlantia nor ACS's interest for the price to escalate. Both companies are loading themselves with debt to make their bids.

"It's positive news since instead of a bidding war there will be a division of assets," said Stefano Fabiani, fund manager at Italy's Zenit, who does not own Atlantia shares. "It certainly reduces the financial burden, which will help Atlantia's share price," he added.

The Spanish market regulator is expected to clear Hochtief's offer in the coming days. Hochtief and Atlantia's bids will then run in parallel for one month during which both groups have the option to improve their proposals.

(Additional reporting by Andres Gonzalez in Madrid and Stephen Jewkes in Milan; writing by Francesca Landini and Sonya Dowsett; Editing by Adrian Croft)

By Paul Day, Francesca Landini and Stefano Bernabei