CHICAGO--Joining the list of Mexican banks looking to expand their franchises north of the border, Banco del Centro SA plans to enter the American market next year, according to a bank official.

Luis F. Cervantes, the Mexico City-based bank's executive vice president, said its parent, Multivalores Financial Group, would open a brokerage firm in New York in 1993, and the bank is weighing whether to expand further in the United States.

Heads Brokerage Unit

"I would not discount having offices in the so-called border states of California, Florida, and Texas," said Mr. Cervantes after a panel discussion sponsored by the Mexican Investment Board in Chicago last week.

Mr. Cervantes also serves as the chief executive officer of Multivalores Casa de Bolsa, the unit that is opening the New York brokerage firm, which will be named Multiva Securities.

Banco del Centro, the last state-owned bank to be sold in Mexico, has $1.5 billion of assets.

Mr. Cervantes' comments follow recent announcements by other Mexican financial institutions targeting lucrative U.S. markets and Mexican-American communities.

Mr. Ricardo Guajardo Touche, chief executive of Bancomer, Mexico's second-biggest, bank with $29.8 billion of assets, said in September it hoped to expand its franchise in the U.S. Southwest.

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