The United States has slammed the Algerian-sponsored resolution as biased against Israel and the official, who spoke to reporters on condition of anonymity, said Washington did not believe it would be successful in lobbying for changes that would overcome the US objections.
"It's very difficult to conceive of changes that would be acceptable to us getting into the resolution," the official said.
Earlier, John Danforth, the US ambassador to the United Nations, predicted that the resolution would fail but declined to elaborate on why. "I would bet ... that this resolution will not pass," he told reporters outside the UN Security Council chambers.
State Department spokesman Adam Ereli declined to make the veto threat public but reiterated US objections to the draft that Danforth made on Monday shortly after Algeria presented it on behalf of the Arab League and the Palestinians.
"The resolution is unbalanced, it is one-sided and doesn't look at all the issues involved in what's going in Gaza at the present time," Ereli said. "We will take this opportunity to convey our concerns to the other members of the council as well as the Palestinians."
He refused to say whether the United States could or would support the resolution or abstain from a vote, which is set for later on Tuesday, if changes were made to the draft.
"If there were changes in it, if it could be balanced in a way, then we might look at it in a different light but, as a general proposition, we believe it is difficult to support a resolution that's unbalanced."
The proposed resolution "demands the immediate cessation of all military operations in the area of Northern Gaza and the withdrawal of the Israeli occupying forces from that area."
It also calls for Israel to grant full access to humanitarian workers in Gaza and urges the Jewish state and the Palestinian Authority to immediately implement commitments outlined in the so-called "roadmap" for peace.
It does not, however, refer to rocket attacks from Gaza by Palestinian fighters onto Israeli soil that the current week-old operation is intended to quell.
The Security Council will discuss the resolution after another day of deadly violence in Gaza as Israel presses ahead with the incursion, the biggest since the Palestinian uprising began four years, aiming to prevent such attacks.
Tuesday's violence, which included an Israeli air strike that killed at least one leading Palestinian militant, raised to 80 the number of Palestinians killed in the Gaza Strip since Israeli forces poured into the north of the territory on September 28.