Officials from German-based Allianz -- one of the world's largest insurance firms -- said that they've atoned for past history and should not be judged by the company's World War II record.
Allianz once insured Nazi death camps and refused to pay life insurance claims to its Jewish clients -- instead granting the proceeds to the Nazis.
The naming rights negotiations between Allianz and the Giants and Jets were first reported by The New York Times, which estimates the potential price tag could reach $20 million to $30 million a year.
Alice McGillion, a spokeswoman for the New Meadowlands Stadium Corp. which is overseeing the construction of the new home of the Giants and Jets, would not confirm details of the negotiations because no deal has been made.
"NMSC has undertaken a rigorous due diligence effort in the consideration of all our potential sponsors and naming rights partners," she said in a written statement.
"In this instance, NMSC management and the teams' owners became sensitive to Allianz's history. This thorough review also found that Holocaust experts, former government officials and leading Jewish and survivor groups believe that Allianz has made determined efforts towards restitution and continues to do so today."
Spokesmen for both teams did not return messages seeking comment.
Peter Lefkin, a senior vice president with Allianz America, said there was an "ongoing discussion" with the Giants and the Jets, but declined to provide any details.
He said the company had been working for the past 65 years to "redress the wrongs of the past, and establish ourselves as a good corporate citizen."
Lefkin cited several Holocaust reparations programs, including the International Commission on Holocaust Era Insurance Claims, that the company has participated in.
"All of these were very much voluntary on the part of Allianz," Lefkin said. "We feel like we've had a moral responsibility to address the wrongs inflicted by the Third Reich, and we've always sought to operate both honorably and transparently in every country in which we have operations."
Several Jewish organizations are opposing the move, saying the company's name is a constant reminder of the past.
The Anti-Defamation League issued a statement calling the proposed naming rights deal "inappropriate" and "an insult to the memory of Holocaust victims."
"The New York region is home to many Holocaust survivors and their families and to World War II veterans for whom memories of the war are still vivid," the statement reads. "We hope that the teams' ownership will take this into account as they move toward a decision on naming rights."
Mark Levenson, the president of The Jewish Federation of Greater Clifton-Passaic -- located in an area of northern New Jersey where many Holocaust survivors live -- said he frequently attends Giants and Jets games and would hate to see the company's name on the new stadium.
"The Holocaust was a pretty unique event, and Allianz had a pretty bad role in that event," Levenson said. "As for reparations after the fact, it doesn't erase how despicable those insurance policy proceeds being paid to the Nazis were. They [Allianz] are in business, and that's OK, but it doesn't mean they are entitled to have their name on a stadium."