Treasury Department officials slammed the door Monday on the possibility that the bailed-out mortgage businesses Fannie Mae and Freddie Mac could return to the private sector, aiming to quash rumors that the Obama administration was considering such a move.

"The right answer is not to 'recap and release' as some say," Treasury Secretary Jack Lew said Monday morning on CNBC.

"Recap and release" refers to the idea that the Treasury would allow the two businesses, bailed out in 2008, to retain earnings to build up capital and then to leave the government's custody.

Some investors in the two companies have pushed for such a maneuver in recent years as legislation to shutter Fannie and Freddie has stalled and their income has picked up. The investors interested in reprivatizing the companies include activist hedge funds.

Lew, however, said Monday that the administration favors "real reform" in the form of legislation that would end the "open-ended risk" that Fannie and Freddie pose to taxpayers.

Taxpayers currently are on the hook for $250 billion in liabilities because of the government's backstop for the companies, he said.

Lew also rejected the claim that the government has been paid back for the $188 billion in bailout funds the government dedicated to Fannie and Freddie in the years after the crisis. Although the businesses since then have sent more than that amount back to the Treasury, especially after the government claimed all of their quarterly profits in 2012, taxpayers are still not square on the deal, Lew said.

"This notion that the slate is clean is just not correct," Lew said, citing the risk that taxpayers assumed.

Antonio Weiss, counselor to the secretary of the Treasury, wrote an op-ed published by Bloomberg View on Monday stating the case against releasing Fannie and Freddie.

Weiss dismissed the argument that the mortgage buyers could rebuild enough capital to operate safely as private companies, citing an analysis from Moody's and the Urban Institute that it would take decades for the companies to save enough earnings to cover potential losses on their combined $5 trillion book of home loans.

While Lew and Weiss rejected the idea of recapitalizing and reprivatizing the companies, legislation to close them and reform the housing finance system has failed in Congress, and key lawmakers see no prospect for passage during Obama's tenure.

Sen. Bob Corker, R-Tenn., the author of a measure to reform the housing finance system, warned this month that, without legislation, the government will continue to face pressure to allow Fannie and Freddie to return to their old form of business.

"If Congress continues to be inept ... [the hedge funds] will eventually take advantage of the system," Corker said in a CNBC interview.

Corker, with a bipartisan group of senators, has more recently sought to advance legislation that would formally forbid the administration from selling its stake in Fannie and Freddie without reform.