Stanford University, which lost a quarter of its endowment last year, has put on the block as much as $1 billion of hard-to-sell investments ranging from private equity to real estate to timberland as it seeks to raise cash, according to people familiar with the matter.

The effort by the $12.6 billion endowment, one of the nation's largest, will test the market for some of these illiquid investments, which have battered the nation's most prestigious universities by tying up cash to fund school operations and other needs. This...