Prime Minister Boris Johnson is due to speak to engineering firms on Monday about whether they can shift production lines to building NHS ventilators.
It comes amid growing concern about a shortage of the life-saving equipment as coronavirus infections increase.
Carmakers and the construction equipment firm JCB are among manufacturers to be contacted.
Downing Street said it wanted the manufacturing sector "to come together to help the country".
"Preparing for the spread of the coronavirus outbreak is a national priority and we're calling on the manufacturing industry and all those with relevant expertise who might be able to help to come together to help the country tackle this national crisis," Downing Street said.
"We need to step up production of vital equipment such as ventilators so that we can all help the most vulnerable, and we need businesses to come to us and help in this national effort."
However, BBC business editor Simon Jack said that manufacturers were far from ready to switch production.
One company told him that comparisons with the accelerated production of Spitfire aircraft during World War Two were misplaced as there was no accepted design nor guarantee components could be sourced quickly.
It is understood one subject on the agenda during the prime minister's talks with industry on Monday is whether specialist firms that make ventilators and other critical equipment might be prepared to share their intellectual property.
Engineers have already been asked to draw up plans to quickly produce more ventilators. And on Sunday evening, Tory MP Tom Tugendhat tweeted: "The Prime Minister is calling for a National Effort for Ventilator production. We have been inundated with offers.
"If you produce ventilators please call the BEIS Business Support helpline on 0300 456 3565. A specific team receiving these calls will start at 10am tomorrow."
On Sunday's BBC Andrew Marr show, Health Secretary Matt Hancock said engineering firms should consider switching some manufacturing to help ramp production of the vital equipment. He accepted it was the kind of policy normally reserved for times of war.
"We've got high quality engineering in this country," Mr Hancock said. "We want anybody who has the manufacturing capability to turn to the manufacture of ventilators, to do that."
Ventilators are vital in the treatment of patients whose lungs have been attacked by the infection. The health secretary told Sky News that the country currently has 5,000 ventilators but said it would need "many times more than that".
But questions remain over how engineering firms with no experience of producing ventilators will be able start manufacturing the complex medical devices.
In a statement on Sunday, the chairman JCB, Lord Bamford, said: "We have been approached by the prime minister to see if we can help with the production of ventilators.
"We have research and engineering teams actively looking at the request at the moment," he said.
However, he continued: "It's unclear as yet if we can assist, but as a British company, we will do whatever we can to help during the unprecedented times our country is facing."
What is a ventilator?
- A ventilator is a machine that helps a person breathe by getting oxygen into the lungs and removing carbon dioxide
- Ventilators can be used to help a person breathe if they have lung disease or another condition that makes breathing difficult. They can also be used during and post-surgery
- A tube, connected to a ventilator machine, is placed in a person's mouth, nose or through a small cut in the throat (called a tracheostomy)
Manufacturing firm, Unipart, confirmed that it was involved in the discussions and aero-engine maker Rolls-Royce said it was "keen to do whatever we can".
It is not just manufacturing firms that have offered their services. Hotel chain Best Western has said it could turn its properties into temporary hospitals if the NHS needed additional bed space during the coronavirus outbreak.
The company said it had seen a surge in cancellations over the last month due to the outbreak.
"If the NHS wants additional bed space, and we can partner with other companies to provide the right medical equipment and supplies, and we can do it safely, then we would be willing to start having those conversations immediately," the hotel chain's boss, Rob Paterson, said.
Manufacturers asked by the government to produce thousands of ventilators to help save the lives of seriously affected victims of coronavirus are not ready to fill the demand.
Although firms including JCB, Unipart, Rolls-Royce and others are in close conversation with the government, no detailed blueprint for increased manufacture of the life-saving equipment currently exists.
One manufacturer told the BBC that comparisons with the accelerated manufacture of Spitfire aircraft during World War Two were misplaced, as there was no accepted design. Even if there was, there is no guarantee the components could be sourced in time to even start production in the next two months.
Ventilators are vital as medical experts estimate that between 10% and 20% of those who succumb to the virus will need critical care. Many of those will need help breathing.
Although firms stand ready and able to produce more ventilators, a lack of clarity on design specifications and component sourcing mean that production remains many weeks away.