The Yankees pitcher made the request Sunday during a private luncheon after attending Mass with his family at St. Patrick's Cathedral.
The cardinal is open to the idea but nothing has been scheduled, Joseph Zwilling, a spokesman for the New York Archdiocese, said Monday.
Whether the cardinal officiates over the christening of Yahuamara, 8, and Steffi, 3, will depend on the family's travel plans while they are in the United States on a visa, Zwilling said.
Last week, Hernandez's daughters, ex-wife and mother were granted permission by the State Department to come to the United States for six months. They were reunited with the player just in time to help him celebrate the Yankees' World Series victory during a ticker-tape parade Friday.
They had not seen each other since December when Hernandez and his current wife, Noris Buoch, fled Cuba in a small boat. He signed a contract with the Yankees in March.
The children and their mother and grandmother arrived in New York after O'Connor personally intervened on their behalf to Cuban President Fidel Castro. The 29-year-old pitcher had asked the cardinal to help bring his family to America.
Zwilling said that if the cardinal did perform the Baptism, the family and godparents would first have to attend a preparatory session because ``Baptism is not a social event, it's a sacrament.''
Hernandez's publicist, Rene Giun, said Monday he did not know if the godparents had been picked. He explained that the children had not been baptized into the church because of religious suppression in Cuba, which began letting up only after the Pope visited Cuba in January.
Guin declined to comment on whether the family would apply for an extension of their visa.
``They're enjoying their visit here. There's no decision at this point in time'' on whether they will ask for an extension, he said.
Guin said the family would remain in New York until Thursday and then travel to Miami. They also planned to visit Disney World and other areas of the United States.
During the Mass on Sunday, O'Connor said the Cuban leader ``has stated explicitly that the family is free to return to Cuba'' if they want to.
An Immigration and Naturalization Service spokesman, Andrew L. Lluberes, explained that the ``derivative status visa'' under which the daughters arrived was valid for as long as their father's non-immigrant visa was valid.
Hernandez was issued a type of non-immigrant visa given to internationally recognized athletes, after the Yankees petitioned on his behalf as his employer. It is good for five years and can be renewed.
The Yankees also can apply on his behalf for an immigrant visa, which is a permanent visa or green card.
Hernandez was an important player for the Yankees this year, with a 12-4 record during the season and a 2-0 mark in the postseason.
The children's mother and grandmother received permission from U.S. Attorney General Janet Reno for ``parole into the United States from Cuba,'' which they can renew for another six months.
After a stay of one year in the country, Lluberes said they can apply under the Cuban Adjustment Act ``for adjustment of their status to lawful permanent residence.''
Lluberes said he did not know if the family was interested in extending their stay, saying, ``I don't know. When the celebrations are over they may want to go back to Cuba.''
© Copyright 1998 The Associated Press