The Reuters news agency said that Gantz, who is the country's alternate prime minister, estimates the health crisis could last another 18 months.
A source in Gantz's party quoted him as telling the US officials on Monday - Ambassador David Friedman and White House adviser Avi Berkowitz - that the July 1 target date was "not sacred".
Last week, Palestinian Islamist group Hamas said that the annexation would be considered a "declaration of war" and warned that Israel will pay an "unprecedented price" if it goes ahead with the plan.
In remarks broadcast later on Monday, Gantz told members of his centrist Blue and White party that "what is not corona-related will wait until the day after the virus".
Worldwide condemnation of the possible Israeli annexations has mounted ahead of July 1, when Israel could take its first steps towards implementing part of a United States-proposed Middle East plan.
Addressing Likud lawmakers, Netanyahu said Blue and White was "not the decisive factor this way or the other", according to a spokesman.
Tensions between Netanyahu and Gantz were on display Sunday at the opening of the weekly cabinet meeting, in an exchange caught on a hot mic about whether Gantz would be able to speak in front of reporters, as he had requested.
"President Trump's plan doesn't really change the reality on the ground".
US ambassador to Israel David Friedman during a visit in the Jewish settlement of Efrat in Gush Etzion
Gantz was quoted by Israeli media as saying that Netanyahu's target date of this Wednesday is not "sacred". "It's very reminiscent of the government I sat in [in 2013-2015], except that Netanyahu didn't demean me, simply because he couldn't". The Committee for Justice and Peace in the Middle East had made an appeal earlier to protest at Place Clairefontaine.
United States ambassador to Israel David Friedman during a visit in the Jewish settlement of Efrat, in Gush Etzion, February 20, 2020.
The Trump proposal - rejected outright by Palestinian leaders - also envisages creation of a Palestinian state, under strict conditions.
Israeli Prime Minister Benjamin Netanyahu is determined to begin the annexation of key parts of the West Bank area on July 1.
She said deepening Israel's control of West Bank land would likely harm Palestinian freedom of movement, turn Palestinian population centers into "enclaves" and clear the way for Israel to "illegally" expropriate Palestinian land. Netanyahu has said Palestinians in these areas would not get Israeli citizenship.
Israeli Prime Minister Benjamin Netanyahu, a strong supporter of Trump, has been unswayed by the worldwide criticism.
A Channel 13 news report earlier this month said that Friedman, who had flown back to the USA for the meetings before returning to Israel, strongly backs Netanyahu's declared intention to go ahead with the move starting July 1, but Kushner was said to be more ambivalent. The plan has also come under surprising criticism from West Bank settler leaders, who believe it does not go far enough and say that any plan that envisions even a watered-down Palestinian state must be opposed.