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By Trevor Hunnicutt

Sept 7 (Reuters) - The California Public Employees' Retirement System (CalPERS) is in talks to outsource its private equity business to BlackRock Inc, according to a person familiar with the matter.

The largest U.S. pension fund's discussions with BlackRock about managing some or all of its private equity investments are at a preliminary stage and may not result in a deal, the person added.

Private equity has been CalPERS' best-performing asset class in the past two decades and accounts for about $26 billion of its portfolio.

But CalPERS, under increasing pressure to achieve higher returns, has been criticized for accepting the high fees and limited disclosures typically associated with the asset class.

The fund said in July it was considering making direct investments in private companies, a potential shift in strategy to improve returns on their investments, in part by cutting fees.

"No decisions have been made. We are still looking at models to bring back to the board," a spokeswoman for CalPERS said on Thursday.

BlackRock declined to comment.

Bloomberg reported CalPERS's discussions with New York-based BlackRock earlier on Thursday.

(Additional reporting by Ismail Shakil in Bengaluru and Robin Respaut in San Francisco; Editing by Leslie Adler and Andrew Hay)