The report said on Monday that the legislation could include sanctions against certain ICC officials.
Israeli Prime Minister Benjamin Netanyahu reportedly asked President Joe Biden to intervene to try to block any potential arrest warrants against Israeli officials.
Earlier in the day, the White House said the ICC has no jurisdiction and does not support its investigation.
Earlier on Monday, US media reported, citing an Israeli official familiar with the matter, that the ICC may issue arrest warrants for Netanyahu, Defense Minister Yoav Gallant, and other senior officials as early as this week.