US citizen Omar Shakir, the New York-based rights group's director for Israel and the Palestinian territories, denies the claims and accuses the Israeli government of seeking to suppress dissent.
Shakir's deportation, expected in the afternoon, would be the first from inside the country under Israel's controversial 2017 law allowing the expulsion of foreigners who support a boycott, according to authorities.
The European Union, United Nations and others have criticised the looming expulsion, with the UN warning of a "shrinking space for human rights defenders to operate" in Israel and the Palestinian territories.
But the United States, Israel's closest ally, declined to do so, saying Sunday only that it supported freedom of expression.
The rights group said Shakir would continue in his position despite being expelled, working from neighbouring Jordan.
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