(CNN) A White House official said Wednesday that White House staff are continuing to look at a variety of options for President Donald Trump 's State of the Union address next Tuesday, another sign of the roiling showdown between Trump and House Speaker Nancy Pelosi over the speech.

The official said options include speeches at the White House or perhaps outside of Washington. The official declined to shed light on what specifically is being discussed.

"If the speaker disinvites, all options are on table," the official said.

Pelosi and Trump have been at odds since Pelosi asked Trump last week to postpone the State of the Union address or deliver it writing, citing security concerns over the government shutdown , which has left about 25% of the federal government unfunded -- including the Department of Homeland Security -- since December 22. Trump responded by canceling Pelosi's use of military aircraft to travel overseas.

The White House said Tuesday it was forging ahead with plans for Trump to deliver his address at the Capitol next week, a senior White House official told CNN, even as Pelosi still appears entrenched in her request for Trump to postpone the speech.

The House speaker's office said earlier Wednesday the White House has never responded in writing to Pelosi's letter suggesting postponement of the speech. Trump has not spoken with Pelosi since the January 9 meeting that Trump abruptly left in the White House, according to an aide familiar with the matter.

Pelosi spokesman Drew Hammill also told CNN that the speaker has never received an official acceptance of the initial invitation to the President to deliver the speech January 29, after she initially invited Trump to do so on January 3, the first day of the new Congress.

Both Pelosi and House Majority Leader Steny Hoyer advised members not to bring family to Washington next week, an implication that the State of the Union is not going to happen, according to a source in the Wednesday morning caucus meeting.

"It's absolutely not clear in terms of what his present intention is, but I can say that unless the government is reopened, it's highly unlikely the State of the Union is going to take place on the floor of the United States House of Representatives," said Rep. Hakeem Jeffries, a member of Democratic leadership, during a news conference Wednesday.

Trump appeared to suggest in a tweet that there had been "written acceptance" of Pelosi's offer to give the speech in the House Chamber, but according to Hammill, no written acceptance has been received.

"Nancy, I am still thinking about the State of the Union speech, there are so many options -- including doing it as per your written offer (made during the Shutdown, security is no problem), and my written acceptance. While a contract is a contract, I'll get back to you soon!" Trump tweeted Sunday

Asked about the acceptance letter, White House press secretary Sarah Sanders said the proper authorities had addressed Pelosi's issues.

"The United States Secret Service and the Department of Homeland Security who would have jurisdiction over whether or not the capital is safe for the President to visit have addressed those concerns," Sanders said. "I think they're the most qualified people not only to address it -- but to make that assessment and they've certainly addressed that and I think satisfied those concerns."

Over the holiday weekend, the White House asked for -- but was denied -- a walk-through by the House of Representatives' sergeant-at-arms in preparation of the speech.

White House officials have continued working on the President's speech and have been mulling other plans for its delivery in the event Trump cannot address the joint session of Congress next week.

"If the speaker withdraws the invite for (Tuesday), contingencies need to be planned," a senior White House official told CNN's Jim Acosta.

"She invited us. We accepted," another official said of Pelosi. "She cited security concerns. (The Department of Homeland Security) responded to those. And we are moving forward."

But regardless of the White House's preparations, Trump will not be able to deliver his State of the Union address before a joint session of Congress unless the House and Senate pass resolutions convening the session. Officials have been weighing alternative venues -- including delivering the speech outside of Washington at a political rally -- but are waiting to gauge Pelosi's next move.

This story has been updated with additional developments Wednesday.