Unidentified judicial sources told Ahram Online Mubarak had requested a transfer to Maadi Military Hospital on release from prison.
Mubarak supporters gathered outside the prison ahead of the deposed leader's release after more than two years in prison.
He will be held under house arrest, Interim Prime Minister Hazem el-Belawi's office said Wednesday night.
"In the context of the emergency law, the deputy military commander issued an order that Hosni Mubarak should be put under house arrest," the statement said.
Belawi's statement came hours after a Cairo appeals court ruling ordered Mubarak's release pending further investigations on charges of illegally receiving expensive gifts from the state-owned Ahram publisher, Ahram Online said.
He had been ordered freed pending trial in two other cases, including a retrial on charges of complicity in the deaths of 800 protesters in February 2011.
The Obama administration has seen reports about Mubarak's release but had no specific comment, White House spokesman Josh Earnest told reporters aboard Air Force One Thursday en route to New York.
"This is a matter that's winding its way through the Egyptian legal system," Earnest said. "I don't have a specific comment on each step in that process.
"I will say that the revolution from 2011 in Egypt is still fresh in the minds of the Egyptian people and there is little desire [or] evidence on the part of the Egyptian people that they want to turn back the clock to the Mubarak regime," he said.
The United States "stands with the Egyptian people as they seek a government that reflects their will," Earnest said. "And it's why we're working with the interim government to encourage them to go back to a transition to a democratically elected civilian government, and overall, an inclusive political process."
Mubarak's sons, Alaa and Gamal, will remain in prison but will be removed to another facility, Israel Radio said. The two had initially been granted permission to remain in Tora Prison close to their father. They are both facing trial on corruption charges.
Mubarak's overthrow in February 2011 led to popular elections in May and June in 2012. Mohamed Morsi was sworn in as the country's first elected president June 30, 2012. A year later mass protests in the streets led to Morsi's ouster on July 3 and since an interim government led by President Adly Mansour.
The Obama administration is still weighing U.S. policy on providing aid to Egypt, Earnest said.
"This is the subject of ongoing conversation at the White House, of course, but no additional high-level meetings" had been scheduled since one on Monday, the White House said.
He said there have been no phone calls and "no change in terms of our ongoing review of our aid and assistance relationship with Egypt."