More than two years after the government seized Fannie Mae and Freddie Mac, the Obama administration will recommend phasing out the housing-finance giants and gradually reducing the government's footprint in the mortgage market, according to people familiar with the matter.

The administration is expected to include three options for a post-Fannie and Freddie world when it releases a long-awaited proposal for the future of the nation's $10.6 trillion mortgage market, which could come as soon as Friday. Together with federal...