Avner Cohen, an Israeli expert and author, was quoted by the paper as saying that under the deal "the United States passively [accepts] Israel's nuclear weapons status as long as Israel does not unveil publicly its capability or test a weapon".
There is no official accounting of the deal, supposedly agreed in 1969 between Richard Nixon, then US president, and Golda Meir, the Israeli prime minister at the time.
In an interview last week with Israel's Channel 2 media company, Netanyahu spoke of his confidence that Obama's recent remarks on a world free of nuclear weapons would not apply to Israel.
"It was utterly clear from the context of the speech that he was speaking about North Korea and Iran," the Israeli leader said.
"But I want to remind you that in my first meeting with President Obama in Washington I received from him ... an itemised list of the strategic understandings that have existed for many years between Israel and the United States on that issue.
"It was not for naught that I requested, and it was not for naught that I received [that document]."
Although there is no formal record of the understanding - nor have Israeli nor American governments ever publicly acknowledged it - some documents hint at an agreement between the two nations.
In 2007, the Nixon library declassified a July 19, 1969, memo from Henry Kissinger, then national security adviser, that comes closest to articulating US policy on the issue.
That memo says "while we might ideally like to halt actual Israeli possession, what we really want at a minimum may be just to keep Israeli possession from becoming an established international fact".