A pair of insurance companies made a bid for

American Equity Investment Life Holding Co.

AEL 0.46%

last month, in a bet that the small Iowa insurer’s retirement-income products will continue to be popular with conservative savers.

Massachusetts Mutual Life Insurance Co. and the publicly traded

Athene Holding Ltd.

ATH 0.24%

offered American Equity $36 a share in cash on Sept. 8, according to a letter sent to American Equity’s chief executive that was viewed by The Wall Street Journal. At that price, the bid would amount to a value of more than $3 billion.

American Equity has a current market value of about $2 billion, and its shares closed Wednesday at $21.99.

The transaction would be the latest consolidation in the insurance industry, in which Athene has been front and center. Athene was founded in 2009 and specializes in annuities. The company, which is about 35% owned by

Apollo Global Management Inc.,

APO -1.32%

has about $162 billion in assets.

All sorts of insurance products—including annuities and basic life insurance—have been hit hard by more than a decade of low interest rates. With “indexed annuities” like those sold by American Equity, insurers take lump sums from consumers and invest the money, aiming to earn more than they are obligated to pay out.

Athene and some other insurers with ties to asset managers like Apollo have been more comfortable than traditional players in venturing beyond high-quality corporate bonds to turn a profit amid the low-rate environment.

Insurers selling indexed annuities have also been affected by the coronavirus pandemic. Such annuities are typically sold in an old-fashioned way: Life-insurance agents sit down with potential buyers in face-to-face conversations.

As government stay-at-home orders and fear of Covid-19 have made those conversations next to impossible in many parts of the U.S., sales of