Another consolidation wave may be coming to the health insurance industry with Anthem Inc. playing a major role.

Analysts have pegged Anthem as one of three potential bidders for Humana Inc., which is prized for its big presence in the Medicare Advantage program.

Then Monday, the Wall Street Journal reported that Anthem has made a bid for Cigna Corp., the nation’s fifth-largest health insurer by enrollment. Aetna Inc. has also expressed interest in Cigna, according to multiple reports.

Amid all the speculation, analysts agree the health insurance industry is ripe for consolidation.

“Like many industries, we think the managed care industry will evolve to a Big 3,” said Ana Gupte, a healthcare analyst at Leerink Partners. “One of the reasons that we think a wave of consolidation is overdue is that we view the industry as being too fragmented.”

Gupte said if Anthem loses out on Humana, then a deal for Cigna might be more likely.

A spokeswoman for Anthem said the company won’t comment on rumors or speculation.

Shares of Anthem were up $3.58, or 2.2 percent, to $164.31 in midday trading Monday. Cigna shares shot up 11 percent, or $14.91, to $152.23.

Anthem, based in Indianapolis and the largest for-profit health insurer in California, sells policies in 14 states.

Anthem had annual revenue of $73 billion and profit of $2.6 billion last year. It had 38.5 million members in March, second only to UnitedHealth Group Inc.

Any merger wave in the industry could also sweep up insurer Health Net Inc. and insurer Molina Healthcare Inc.