In newly-released excerpts of the testimony of former US Special Representative to Ukraine Kurt Volker to Congress, Volker said that President Donald Trump's personal attorney Rudy Giuliani served as both a "conduit" to Ukraine and demanded they announce investigations that would be politically favorable to Trump. It is uncertain if Mulvaney will appear.
The White House did not immediately respond to Fox News' request for comment.
Sondland is Trump's ambassador to the European Union, a key figure in the Ukraine business since he had direct contact with both Trump and Ukrainian officials. Some who have been subpoenaed have testified, while others have refused.
Democrats also made all the text messages Volker provided to House committees public on Tuesday.
The depositions of Volker and Sondland - who, along with Energy Secretary Rick Perry, referred to themselves as the "three amigos" placed in charge of Ukraine policy - are anticipated on Capitol Hill for different reasons. He testified to the House Foreign Affairs, Intelligence and Oversight panels for more than eight hours behind closed doors on Oct 3.
Gordon Sondland, the United States ambassador to the European Union, had initially denied any knowledge of a link between the $391 million in aid and Mr Trump's request that Ukraine launch an inquiry into his political rival.
President Donald Trump makes his way to board Air Force One before departing from Andrews Air Force Base in Maryland on November 4, 2019.
In their interviews, Yovanovitch and McKinley said the State Department was being used for domestic political purposes under Trump and warned that would hurt American interests.
In a letter sent Tuesday afternoon, the House Democrats leading the impeachment inquiry said they want to learn what Mulvaney knows about Trump's efforts to press for an investigation into former vice president Joe Biden and his son Hunter Biden, who sat on the board of a Ukrainian gas company.
Trump froze almost $400m in U.S. military assistance to Ukraine shortly before speaking to Zelenskyy, prompting accusations from Democrats that he had misused taxpayer dollars destined for a vulnerable USA ally for personal gain.
'Specifically, the investigation has revealed that you may have been directly involved in an effort orchestrated by President Trump, his personal agent, Rudolph Giuliani, and others to withhold a coveted White House meeting and almost $400 million in security assistance in order to pressure Ukrainian President Volodymyr Zelensky to pursue investigations that would benefit President Trump's personal political interests, and jeopardized our national security in attempting to do so, ' it continued. Trump on Sunday said that Republicans should release their own transcripts, even though each witness will have a chance to review the official transcript to ensure accuracy.
The White House has instructed its officials not to comply with the impeachment inquiry being led by House Democrats. Trump would not be removed from office unless two-thirds of the senators who are present vote to convict him - an unlikely prospect at this point.
Sondland testified that it would be "improper" for Giuliani to push the Ukrainians to investigate Biden or get involved in the 2020 election. "There's going to be political influence in foreign policy", Mulvaney said.
But if history is a guide, the administration has not been cooperative.
It is unclear, at this point, whether Mulvaney will appear before the committees on Friday.