Tomblin spokeswoman Amy Shuler-Goodwin said during Tomblin's meeting with Sebelius, the governor told the secretary West Virginia would wait until the actuarial study was completed before making a decision.
He also expressed concerns that the state's insurance commissioner had not received rules on how the Affordable Care Act's health insurance exchange plans would work, Goodwin said.
Even some Republican governors who once staunchly opposed the broadening of Medicaid coverage now are publicly embracing it.
New Jersey Gov. Chris Christie, one of the country's most well-known Republicans, announced Tuesday he would expand his state's Medicaid program. Last week, Gov. Rick Scott of Florida said he also would embrace the expansion.
The federal government has promised to pay 100 percent of additional Medicaid costs for the first three years of the expansion, with states picking up part of the bill after that time.
More than 400,000 West Virginia residents currently are on Medicaid.
West Virginians for Affordable Health Care released a report earlier this week that claims expanding the government insurance program would create an additional 6,200 jobs and add $664 million to the state's economy by 2016.
The Associated Press also contributed to this report.