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, 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."
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."
