The Obama administration will propose raising the cost of loans backed by the Federal Housing Administration as part of a plan to reduce government support of the mortgage market to below 50 percent, said sources familiar with the plan.

Under the tentative proposal to overhaul the U.S. housing finance system, the White House is considering shrinking Fannie Mae and Freddie Mac's $1.5 trillion mortgage portfolios within 10 years, said the sources.

The government currently backstops more than 85 percent of the $10.6 trillion mortgage market through the Federal Housing Administration (FHA) and the taxpayer-funded mortgage buyers Fannie Mae and Freddie Mac.

The plan being considered would give the private sector a dominant role in the housing market and reduce the government's support to below 50 percent within five to seven years after the plan is adopted, said the sources.

Key housing officials including Treasury Secretary Timothy Geithner were scheduled to meet at the White House on Tuesday to finalize the long-awaited proposal to overhaul the housing finance system, the sources said.

The sources requested anonymity because the proposal has not been made public and could still change. A Treasury Department spokesman declined to comment because the report has not been released yet. The report is expected to include several options and is scheduled to be released on Friday, an industry source said.

As part of its proposal, the administration is considering backing a scheduled decrease in the so-called conforming loan limit, a cap on the size of mortgages that FHA, Fannie Mae and Freddie Mac can guarantee, the sources said.

The loan limits are set to fall from $729,500 to $629,500 at the end of September. The sources added that the administration may take further steps to reduce the loan limit.

Fannie Mae and Freddie Mac provide liquidity to the mortgage market by buying mortgages from lenders and repackaging them as securities, which they guarantee. But as the housing market crumbled, the government took control of Fannie Mae and Freddie Mac and since 2008 has injected more than $150 billion in taxpayer funds to prop them up.

Republicans have called for winding down the companies and eliminating federal guarantees of mortgages, forcing a reliance on the private market to finance housing.

(Additional reporting by Margaret Chadbourn)

(Reporting by Corbett B. Daly, Rachelle Younglai; Editing by James Dalgleish, Andrew Hay and Diane Craft)