The Senate GOP Conference chairman told CNBC on Wednesday he plans to propose such an amendment to the House Republican health-care proposal.
Thune, the third-ranking Republican in the Senate leadership, said on "Squawk Box" he's aiming to "improve upon" the House plan by redirecting the tax credit to the "lower end of the income scale" and providing "an age adjustment so that older people, people of lower incomes are better able to afford health insurance under this new plan."
The House GOP plan seeks to support the purchase of individual health plans with tax credits instead of subsidies. However, the value of the Republican tax credits, unlike under Obamacare, are tied to a customer's age rather than income. Credits under the House plan would not adjust for income or for the cost of insurance plans.
The means test would help get more support from senators who are worried that the House bill does not do enough to protect the less fortunate and the elderly from spiraling costs, said Thune. "I have a number of colleagues who share my view about the tax credit and how the benefit is distributed," he said.
The Congressional Budget Office said Monday that while premiums would likely be significantly lower under the GOP plan, the Republican proposal would "substantially" raise premiums for older people and would reduce subsidies for lower-income Americans.
The South Dakota senator acknowledged the politics at play to getting those on the fence on board. "I think this is a negotiation. The political dynamic is different in the House than they are in the Senate," Thune said. Republicans hold 52 of 100 seats in the Senate.
On the flip side, some conservative House members believe the current bill keeps too much of Obamacare.
Correction: This story was revised to correct that there are 52 Republicans in the Senate.