NEW YORK (TheStreet) -- Aetna ( AET) has put its pharmacy-benefit management business up for sale, a report says, and industry competitors such as CVS Caremark ( CVS) and Medco Health Solutions ( MHS) are taking a look.

The Wall Street Journal, citing people familiar with the matter, reports Aetna's business has been shopped around by bankers at Bank of America Merrill Lynch and Credit Suisse.

The business, which manages prescription-drug benefits for more about 11.2 million members, has been up for sale for a couple months, but no final deal or announcement is likely soon, these people say, the newspaper reports.

The business also was shopped to Express Scripts ( ESRX), which purchased WellPoint's ( WLP) NextRx pharmacy-benefit business for $4.68 billion in April, the Journal notes.

An analyst report in April estimated Aetna could get at least $2 billion for the pharmacy-benefit business, the Journal notes.

The insurer moved up its second-quarter earnings announcement by two days to Monday though it wasn't clear if the move was tied to the auction process, the Journal reports.

Reported by Joseph Woelfel in New York.

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