UnitedHealth Group Inc. has approached Aetna Inc. about a takeover deal that would likely be valued at more than $40 billion, according to people familiar with the matter, the latest move in a frenzy of merger talks in the health-insurance industry

The approach, in the form of a letter, came within the past few days, according to one of the people. It isn’t clear what, if any, the response was, and it is far from certain there will be any deal between the companies.

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