The U.N. has so far stayed clear of hedge funds even as many large institutional investors have embraced them.
The California Public Employees' Retirement System, the nation's largest pension fund, made waves in September when it said it planned to cut most of its hedge funds. But industry assets have continued to climb thanks to fresh cash from other pensions, endowments and other institutional investors.
Read MorePensions stick with hedge funds despite CalPERS exodus
"They would be well served by adding hedge funds," said Michael Weinberg, a hedge fund expert who teaches a class on pension investing at Columbia Business School. "Many other pensions have already seen their value either to improve returns with the same risk as stocks or bonds, or similar returns to them with less risk."
Money from institutions represents 66 percent of the capital invested in hedge funds, according to the Managed Funds Association. Pensions represent the highest percentage of that at 39 percent, according to recent Preqin data. Of the pensions that do invest in hedge funds, public plans allocate an average of 7.8 percent of their portfolios to them; for private sector plans it's 10.5 percent, according to Preqin.
A previous target for alternative investments in the U.N. plan was 6 percent of assets. That figure is being updated by Buck, but a 4 percent allocation to hedge funds, for example, would be more than $2 billion. Tereza Trivell is head of the U.N.'s alternative investing unit.
The U.N. fund, whose investments are led overall by recent appointee Carol Boykin, has 63.5 percent of assets in stocks and 24.5 percent in fixed income, according to a report on the portfolio as of December. It also has 5.2 percent in real assets like real estate, timberland and infrastructure. Just 3 percent is in alternatives, including private equity, commodities and the "risk parity" strategy.
The risk parity allocation is managed by Bridgewater through its All Weather strategy. Dalio pioneered the concept, a conservative mix of asset classes that is designed to perform in any economic environment over the long term. Bridgewater also happens to be the largest manager of hedge funds, which are more trading-oriented and charge higher fees.
A spokesman for Bridgewater declined to comment on if the firm was being considered for the U.N.'s likely hedge fund allocation.
The U.N. pension is more than 90 percent funded, meaning it is still slightly short of having all the cash necessary to fund payments it has promised. That amount is better than many other pensions. The average corporate and public pension plan is about 80 percent funded, according to data from consulting firms Mercer and Wilshire Associates.
The U.N. fund averaged a return of 6.18 percent from 2004 to 2014, according to U.N. materials. That outperformed its policy benchmark return of 5.84 percent (a mix of 60 percent stocks and 31 percent bonds), but was behind global stocks (6.6 percent).
The HedgeFund Intelligence Global Index, representing all hedge fund strategies, gained 5.83 percent net of fees over the same 10-year period.
Read MorePension funding up,but still way short
Funds of hedge funds, the other means in which the U.N. is considering accessing the strategy, are vehicles that allocate to various independent managers for an extra layer of fees. They are a way to gain exposure to multiple hedge funds at once without the hassle of independently selecting and monitoring each manager.
Funds of funds have declined in popularity in recent years given relatively muted returns and concerns around their oversight of managers (some were invested in the Bernard Madoff Ponzi scheme).