A Tory minister has asked Labour MP Frank Field to meet the health secretary, Jeremy Hunt, to discuss his ideas for raising national insurance contributions to pay for the NHS, in a sign that the Conservatives are considering radical options to plug the huge funding gap.

Field told the Observer that he was approached by the minister, who said the financial crisis in the NHS needed to be addressed and that he was right to be floating ideas on how the service could be maintained and put on a sound financial footing for future generations.

Field told the minister he would be willing to meet the health secretary, but not before he had held talks with shadow chancellor Ed Balls about his proposals, which he did last Tuesday.

According to Field, the minister also said that the financial crisis in the NHS had been the subject of discussions at high levels in government in recent weeks.

Field is drawing up proposals that he says will help to fill a looming £30bn a year "black hole" in NHS funding that will occur by 2020.

Without action, he says, a Labour or any other government would be faced with the prospect of having to make swingeing cuts across the other public services, far deeper than envisaged so far, to maintain the NHS in anything like its current form.

Field said: "A Conservative minister approached me and said they had been talking about the NHS's financial crisis and my ideas on how to address it within the department.

"The minister said it would be a good idea to go along and talk to the health secretary about it and agreed that something had to be done."

Some Conservatives now believe that drastic action needs to be taken on NHS funding, and regret that David Cameron has not proposed some form of NHS tax to underpin his commitment to maintaining the current service free at the point of use. The chancellor, George Osborne, however, is known to be strongly opposed to any move that would compromise a Tory general election message based around the idea of lower taxes, and is said to believe that radical options can be delayed until the next parliament.

Recent figures, based on data from NHS England and the Nuffield Trust and produced by the Commons library, suggest that NHS costs alone will go from £95bn a year now to more than £130bn a year by 2020.

As a result, Field argues that a 1% rise in national insurance, similar to that ordered by Gordon Brown to pay for increased spending on the NHS in 2002, would be welcomed by the public if it was guaranteed that the money would be spent specifically on health and social care.

In his meeting with Balls, which he described as "very friendly and constructive", Field said that any rises in national insurance on top of an initial emergency increase, should be matched with an accompanying pledge to reduce income tax by the same amount – meaning that deep cuts would have to be made elsewhere.

The Observer revealed last month that Field's ideas were being fed into Labour's policy review. Balls has been opposed to such a move, fearing it would leave Labour open to charges that it is returning to a high-tax agenda. At Tuesday's meeting, Field explained how radical his proposals are – a progressive national insurance base to raise revenue, to be matched by tax cuts.

Signs, however, that the Tories are interested in the Field plan suggests they may be examining ways to outflank Labour, and leave it vulnerable on an issue regarded as one of its strongest.

Field said the extra NI contributions should go into a dedicated fund that would be run as a mutual, with elected members negotiating each year's level of contributions. "What we need is a new settlement for the NHS, an NHS mark two, that will reassure people that the most popular public service is safe for future generations." He is now concerned that unless Labour moves on the issue, the Tories will steal the idea. Field proposed the sale of council houses in 1979, only to see Margaret Thatcher take up the idea and turn it into one of her most emblematic policies.

Labour is already committed to combining the budgets for health and social care but the party's public position thus far has been that it will not look at a specific NHS tax.

Shadow health secretary Andy Burnham is wary of increasing NI in a way that would mean younger people in work having to pay the care costs of those already of pensionable age.

He favours other options, including a plan floated by Labour before the last election for a levy of 10% to 15% on people's estates after death to pay care costs. To address Burnham's concerns, Field proposes that those now over pension age would be asked to continue to pay NI, if they wanted free care. Otherwise, they would have to pay under the current system.