The report said 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.
The US Ambassador to the United Nations Linda Thomas-Greenfield said that the United States does not interfere in the work of the ICC amid concerns over the possibility the ICC may issue arrest warrants for senior Israeli officials.
"It's an independent organization and their efforts are being undertaken without any contact or interference by the US," Thomas-Greenfield said in a press briefing.
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.