The Obama administration is considering an overhaul of Fannie Mae and Freddie Mac that would strip the mortgage finance giants of hundreds of billions of dollars in troubled loans and create a new structure to support the home-loan market, government officials said.

The bad debts the firms own would be placed in new government-backed financial institutions -- so-called bad banks -- that would take responsibility for collecting as much of the outstanding balance as possible. What would be left would be two healthy financial companies with a clean slate.

The moves would represent one of the most dramatic reorderings of the badly shattered housing finance system since District-based Fannie Mae was created by Congress to support mortgage lending during the Great...