These states are home to senators who are under pressure on healthcare. Both of Alaska's Republican senators, Lisa Murkowski and Dan Sullivan, are still on the fence over Graham-Cassidy.
The CMS had no immediate comment on the Axios report.
Besides McCain, Kentucky's Rand Paul is the only other Republican senator who has publicly said he opposes the bill.
Maine's Susan Collins said she was leaning against the bill, the Portland Press-Herald newspaper reported on Friday. Kansas' Jerry Moran is also undecided.
No Democrats support the bill.
To pass Graham-Cassidy, the Republicans need at least 50 votes in the 100-seat Senate, which they control 52-48, with Vice President Mike Pence casting a potential tie-breaking vote.
The insurance industry, hospitals, medical advocacy groups such as the American Medical Association, American Heart Association and American Cancer Society, the AARP advocacy group for the elderly and consumer activists oppose the bill.
The Center on Budget and Policy Priorities, a liberal think tank in Washington, estimated the bill would cause more than 30 million people to lose insurance.
Late night television host Jimmy Kimmel, who criticized the Graham-Cassidy legislation on his show, thanked McCain on Twitter. Kimmel made himself part of the healthcare debate in May when he emotionally discussed his newborn son's emergency heart surgery. "Thank you @SenJohnMcCain for being a hero again and again and now AGAIN," he tweeted. (Reporting by Susan Heavey and Susan Cornwell; Additional reporting by Roberta Rampton; Writing by Frances Kerry; Editing by Kevin Drawbaugh and Leslie Adler)
This article was provided by Reuters.