Mr Trump made the claim during his daily press briefing on the outbreak at the White House on Monday.
He said the UK made the urgent plea, as ministers scramble to boost capacity for the sickest of patients.
The United States currently has the highest number of confirmed coronavirus cases worldwide.
Mr Trump told repoters: "The UK called today and they wanted to know would it be possible to get 200.
"We're going to work it out, we've got to work it out.
He added: "They've been great partners. They wanted 200, they need them desperately."
Mr Trump's claim comes a day after defence firm Babcock said it had received a Government order to produce 10,000 ventilators.
The Government has said 30,000 ventilators will be needed for the NHS to cope with the peak of the Covid-19 pandemic.
The President also extended his support to Boris Johnson who has spent a second night in intensive care for coronavirus symptoms.
Mr Trump said: "We pray for Prime Minister Boris Johnson, who's become a great friend of ours. He loves this country, he loves his country, but he loves the USA.
He added: "He's always been very good to us. Whenever we had difficulty, he was with us and we appreciate it. So we pray for Prime Minister Boris Johnson, he's going through a lot."
Coronavirus: Everything you need to know