A source in Gantz's party quoted him as telling the USA officials on Monday - Ambassador David Friedman and White House adviser Avi Berkowitz - that the July 1 target date was "not sacred".
A Channel 13 news report earlier this month said that Friedman, who had flown back to the United States 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.
Briefing reporters last week, Gantz - who serves as Israel's defence minister, as well as alternate prime minister - predicted that the coronavirus crisis could last 18 months.
In public comments later in the day, Gantz appeared to refer to annexation again when he said at a Blue and White faction meeting that "those things that are not related to the fight against coronavirus will wait until the virus is behind us".
In response, Netanyahu told legislators from his right-wing Likud party that annexation steps due to be debated by the cabinet as early as Wednesday did not depend on Gantz's support.
"We are in talks with the U.S. team here in Israel", Netanyahu said at a Likud faction meeting in the Knesset. "They are not a factor either way".
Worldwide condemnation of the possible Israeli annexations has mounted ahead of July 1, when the Jewish state could take its first steps toward implementing part of a US-proposed Middle East peace plan.
"Annexation is illegal. Period", Bachelet said in a statement.
Bachelet urged Israel to shift course, warning that "the shock waves of annexation will last for decades, and will be extremely damaging to Israel, as well as to the Palestinians".
Over the last four years, Trump has reversed decades of USA policy by declaring Jerusalem as the capital of Israel and recognising Israel's claim of sovereignty over the Golan Heights.
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.
The Palestinians, with broad global support, want to retain the territory as the heartland of their future independent state.
Global opposition has mounted in the past few weeks, with Palestinian leaders, the United Nations, European powers and Arab countries allied with Israel all denouncing any annexation of land that Israeli forces captured in a 1967 war.
U.N. Special Rapporteur on Human Rights in the Palestinian Territories Michael Lynk has urged the European Union to take real and drastic steps against Israel if Jerusalem moves forward with its plans to extend its sovereignty over the Jordan Valley, and parts of Judea and Samaria, and called upon the European body to "develop a menu of countermeasures".
Israel's foreign ministry reacted angrily to the statement, noting that it was "not the first time" that Bachelet "has politicised her office against Israel, in a one-sided manner".