A senior Trump administration official told Fox News Thursday that "there is still some work to do" to gain the release of three Americans held as prisoners in North Korea, despite a claim by Trump lawyer Rudy Giuliani that the men would be freed that day.

Giuliani told "Fox & Friends" Thursday morning that North Korean leader Kim Jong Un was "impressed enough" with President Donald Trump that he would "be releasing three prisoners today." Giuliani's statement echoed reports by South Korea's Yonhap News, the Financial Times and CNN that the men -- Kim Dong Chul, Kim Hak Song, and Tony Kim -- would be freed soon.

However, the administration official told Fox News that Giuliani had gotten ahead of events on the ground in North Korea. That was confirmed Thursday afternoon by White House Press Secretary Sarah Sanders and State Department spokesman Heather Nauert.

"We can’t confirm the validity of any of the reports currently out about their release," Sanders said, "but we certainly would see this as a sign of good will if North Korea were to release the three Americans ahead of discussions between President Trump and Kim Jong Un."

Said Nauert: "We've certainly been following their cases for quite some time [but] we can't confirm the validity of those reports at this point. We want to see our American citizens brought home. We want them to come home as soon as possible."

Yonhap reported Wednesday that the three men had been moved to a hotel on the outskirts of Pyongyang. The report, which cited South Korean activist Choi Sung Yong, said that the U.S. and North Korea "are known to be in talks over their possible repatriation."

That same day, the Financial Times reported that the men had been released from the labor camps where they had been held since their arrests. That report quoted Choi as saying that "Trump can take them back on the day of the U.S.-North Korea summit, or he can send an envoy to take them back to the U.S. before the summit."

The CNN report, which cited "an official with knowledge of the ongoing negotiations," said that the prisoner release was "imminent."

Late Wednesday, Trump raised hopes even more when he tweeted, "Stay tuned!" at the end of a message about the detainees.

Kim Dong Chul, a South Korea-born U.S. citizen and former Virginia resident, was sentenced in April 2016 to 10 years in prison with hard labor after being convicted of espionage. He reportedly ran a trade and hotel service company in Rason, a special economic zone on North Korea's border with Russia.

Tony Kim was detained at Pyongyang's airport in April 2017 and accused of unspecified "hostile acts" against the North Korean state. He taught accounting at the Pyongyang University of Science and Technology.

Kim Hak Song, an ethnic Korean who was born in China, was detained in May 2017 and also accused of "hostile acts." He worked in agricultural development at an experimental farm run by the Pyongyang University of Science and Technology, which was founded in 2010 with donations from Christian groups.

A fourth American detainee, Otto Warmbier, died in June 2017 -- just days after he was repatriated to the U.S. with severe brain damage. He had been arrested in January 2016 and accused of stealing a propaganda poster and was sentenced to 15 years in prison with hard labor.

Last week, Warmbier's parents filed a wrongful death lawsuit against North Korea in U.S. federal court, alleging that the Kim regime had tortured and killed their son.

Fox News' John Roberts and The Associated Press contributed to this report.