"The meeting was agreed to with Trump first, then we reached out immediately to the Clinton camp for balance," the official told AFP without saying who proposed the first meeting.
Netanyahu is already in New York, where he addressed the UN General Assembly on Thursday.
Analysts say the Israeli premier is trying to avoid any impression of interfering in the American electoral campaign.
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During the 2012 race for the White House, US officials criticised Netanyahu over his perceived support for Republican candidate Mitt Romney.
Romney visited Jerusalem during his campaign and criticised President Barack Obama's policies on the Middle East.
Trump had planned to visit Israel last December, but postponed the trip after his proposal to bar Muslims from entering the United States prompted worldwide condemnation.
In May, he told Israel Hayom, a free daily newspaper seen as close to Netanyahu, that he would visit Israel "soon".