The Health Minister will ask health insurers to put a two-year freeze on their policy prices, it has been reported.
According to The Irish Times, the Government will promise not to increase taxes on the industry over the same timeframe.
The proposal is part of a drive to get more people to sign up for health insurance after a significant drop in subscribers in recent years.
More than 280,000 people have dropped their health policies since 2008 - with almost of a third of them in the 18-29 age bracket.
That rapid decline has led to serious concerns among insurers and the Government about the viability of the market.
Health Minister Leo Varadkar is now said to be seeking a deal with health insurance firms - which will stop them from hiking policy prices for two years.
In exchange, the Government will pledge not to increase stamp duty - the tax the companies have blamed for price hikes for policyholders.
The proposal will be discussed by Cabinet in the coming weeks - alongside a "sliding scale" of discounts on policies for those in the 21-25 age group to try to get more to sign up for health insurance.
However, Dermot Goode of totalhealthcover.ie says it does not address some of the key factors driving up insurance prices.
"The big elephant in the room is claims costs, and as those claims costs keep rising - driven by a shrinking membership base and an older age profile - we're going to see rising claims costs and they have to be passed on to consumers," he said.
"I think what the Minister's trying to do is definitely welcome; I think he might get a 12 month deal if he's lucky, I don't see how the insurance companies can give him a two-year deal."