In a policy paper published today, Mr Willetts, the Tory MP for Havant, proposes six key areas where the private sector could co-operate with the NHS.
However, many of the firms ready to put money into the NHS would not wish to negotiate with the NHS unions, Mr Willetts says in his paper for a conference this month on private-sector opportunities in the NHS organised by the Social Market Foundation, a centre- right think tank.
'The best way forward may be to give private providers the opportunity of tendering for new NHS developments. The political sensitivity surrounding private provision is much reduced if it is manifestly supplying an extra new facility.
'The crucial first step must be for the Department of Health to liberalise its capital control procedures. Local hospitals should have much more freedom to draw on private finance without having to refer the whole scheme up the line.'
He says the hospitals should be given much more freedom to shift spending from plant and equipment to revenue, to enable the NHS to pay for the running costs of units built and operated by private health firms.
Mr Willetts, the former head of the Centre for Policy Studies, who influenced the Government's changes to the NHS, including the introduction of an internal market, says the private sector could lease private hospitals and equipment to the NHS; build private hospitals and care centres for the NHS to run; build and operate units for the NHS; operate complete hospitals; co-operate in primary and community care; and offer shared facilities.
The Treasury's objections to private sector involvement in public sector schemes were dropped in the Chancellor's Autumn Statement, Mr Willetts says in his paper.
'Much of the discussion of this subject over the past few months has concentrated on transport because here tolling could generate a stream of income which would give private investors their return. But there is also scope for attracting private finance even where the service remains free at the point of use, as with the NHS.'
Mr Willetts added: 'The vast majority of the schemes put forward have failed to come to fruition because of a combination of Treasury rules, political caution and exaggerated expectations on both sides. It would be a great pity if this latest initiative were to end up as just another fruitless teasing of the private sector.'
He says the private sector could help to avoid cost over- runs on building new hospitals such as Westminster and Chelsea hospital, which was attacked by the Commons Public Accounts Committee.
'Treasury thinking seems to have changed markedly over the past few months, but it will still want to see a genuine benefit for the NHS from such changes.'
He suggests the Department of Health and health regions should circulate to private firms the proposals put to it for all new hospitals and units.
'The crucial question is really one of managerial and political will. If it is clear that ministers and the management executive (of the NHS) support such developments, there is undoubtedly enormous scope for schemes along these lines.'