Cigna shares fell as much as 4 percent in trading Thursday and were recently down more than 2.5 percent for the day and about 10 percent for the week.
On Tuesday, J.P. Morgan and its partners announced plans to form a venture aimed at lowering its employee health costs. Since then, investors have been concerned that Cigna will be squeezed on pricing for its services or lose business. The company currently insures about 20 percent of J.P. Morgan's employees.
"We're one of J.P. Morgan's service partners, so we have ongoing dialogue with J.P. Morgan on a regular basis," including this week, said Cordani in an interview on CNBC's "Squawk Box."
"We do see this as an opportunity, and we're in the middle of that conversation, as you would expect," he said.
The three large employers said this week that they are hoping to form a separate entity to handle benefits "free from profitmaking incentives," in order to lower health costs and improve service for their workers. Cordani pushed back on the profit implications on the company's earnings conference call.
"We should not view that an industry with medical cost trend (growth) of 5-6-7 percent as sustainable," said Cordani, while pushing back on the notion that insurer profits drive those increases.
"Our industry is capital intensive ... This is not going to get solved with extracting a couple of points out of the (profit) margin," he said.
Cigna reported fourth-quarter adjusted profits of $1.94 per share, 5 cents above consensus estimates from Thomson Reuters. Revenue of $10.5 billion also topped expectations, driven by strong growth in premiums and fees.
Cigna executives highlighted the company's ability to contain medical cost growth to 3 percent on its employer plans last year, well below the industry trend of 5 to 6 percent annual growth.
The executives cited that stat as one of the things, along with the emphasis on integrated care for chronic conditions, as putting them in a strong position to be a partner for the new Amazon-led initiative.
"Clearly (it's) a disruptive headline, and clearly a need of creating clarity in terms of next steps. I think the question fundamentally for everybody in the space is can you grow, can you innovate and can you continue to provide strong value," Cordani said.
The company raised its outlook for 2018, to $12.40-$12.90 per share, based in part on tax reform. The firm said it will use $15 million of the tax windfall to raise its minimum wage for front-line employees to $16 an hour, and $30 million to boost contributions to workers' 401(k) accounts.
Cigna executives said their individual Obamacare market plans made a small profit in 2017; rival Anthem reported similar stabilization in their individual exchange business.