By Christine Murray and Julia Love

MEXICO CITY (Reuters) - Funds controlled by the family of Mexican billionaire Carlos Slim are set to acquire a large chunk of an investment trust to fund Mexico City's new airport, three sources with knowledge of the deal said, as doubts hang over the project's future.

The placement came as leftist presidential frontrunner Andres Manuel Lopez Obrador threatens to scrap the airport and block new work on it. Slim's construction business has been one of the biggest winners of work for the airport.

Slim's Grupo Financiero Inbursa, through vehicles including pension fund Afore Inbursa, was allocated around 13 billion pesos of certificates of the trust created to finance part of the construction of the airport, said the people, who spoke on condition of anonymity.

It represents the largest share of all the investors that participated, the people said, and is more than one third of the 30 billion pesos ($1.62 billion) total raised on Friday by GACM, the company responsible for building the airport.

Inbursa also worked on the deal as one of the underwriters, and it sold on some of the certificates to clients, one of the people said.

The allocation is not final until next week, said one of the people. GACM did not respond to a request for comment. A spokesman for Inbursa declined to comment.

Slim, who is Latin America's richest man, already has the largest airport contract by far, which was awarded to a consortium including his construction firm.

The 85 billion peso ($4.59 billion) contract for the terminal building was for a group including Spain's Acciona <ANA.MC>, Slim's Operadora Cicsa and several Mexican firms, including builder ICA <ICA.MX>.

"Regardless of the financial stakes...I think he is very interested in that the project succeeds," said Alejandro Schtulmann, president of EMPRA, a political risk consulting firm based in Mexico City.

The Slim family owns around 57 percent of the shares in Inbursa, according to its latest annual report.

(Reporting by Christine Murray and Julia Love; Additional reporting by Sheky Espejo; Editing by Leslie Adler)