Although named the Troubled Asset Relief Program -- or TARP -- the program has done a lot of things, but buying toxic assets from banks has not yet been one of them.

The U.S. Treasury has used the TARP funds to buy preferred bank stock and later, in some cases, convert this to common stock. It has used the funds to prop up automotive giants General Motors Corp and Chrysler and bailout American International Group.

But the toxic assets just sat there. Banks have been reluctant to sell the assets considering they might come up in value over time, The Washington Post reported Tuesday.

In July, the Treasury announced a program of combining private and public funds to buy toxic assets, which received a lukewarm response.

The Treasury is expected to announce Wednesday that the first round of funding for the program will be made available, the Post said.

The Treasury expects to start with a $2.5 billion matching fund investment, which could grow to $40 billion over time, the Post said.