Walmart Inc.’s potential acquisition of a health insurer would push it far beyond its big-box roots, enabling it to diversify away from the competitive pressures of retailing yet also thrusting it into a complicated and rapidly evolving health-care sector.

Walmart is holding preliminary discussions to buy U.S. health insurerHumana Inc. and the companies are discussing various options, The Wall Street Journal reported Thursday. There is no guarantee the companies will agree on a merger or pursue some other partnership.

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