The prime minister claimed his red lines for negotiations included any idea of American firms buying parts of the state-funded health service.
He also said the US would have to open its markets to British goods, including lamb and beef, which are barred, and lower its tariffs.
Mr Johnson claimed he would tell the president “that when we do a free trade deal, we must make sure that the NHS is not on the table, that we do not in any way prejudice or jeopardize our standards on animal welfare and food hygiene in the course of that deal, and that we open up American markets.”
He is expected to attempt to lay the groundwork for a trade agreement while meeting Mr Trump this week at the United Nations General Assembly in New York.
Opponents of Brexit fear the NHS will be opened to private US firms as part of trade negotiations and have suggested the UK would have to accept chlorine-washed chicken, which is banned in the European Union.
They have also raised concerns that Britain aims to become a low-tax, low-regulation economy.
When Mr Trump visited London on a state visit this year he told a press conference he believed the NHS would be up for grabs.
Mr Johnson is due to tell US and Canadian business leaders the UK would “roll out the red carpet” for investors after Brexit, his office said.
He will add that “we want a market that is open to the world, with the most competitive tax rates and the best skilled workforce in the hemisphere”.
However, Mr Johnson is also likely to be dogged by the failure to reach agreement on withdrawal from the EU as the 31 October deadline approaches.
The prime minister told reporters he did not think there would be a “New York breakthrough” in meetings with European leaders at the UN, but added: ”I think a large number of the important partners really do want a deal.”
Meanwhile the EU has indicated that Britain has still not come up with proposals for maintaining an open border between Ireland and Northern Ireland.
Chief EU Brexit negotiator Michel Barnier said Monday that “based on current UK thinking, it is difficult to see how we can arrive at a legally operative solution”.
And after meeting the prime minister, European Council president Donald Tusk tweeted succinctly: “No breakthrough. No breakdown. No time to lose.”
The prime minister argues that the border can be kept free of customs posts and other obstacles using a technological solution and an all-Ireland zone for animals and agricultural products.
“I think colleagues around the table in Brussels can see how we might do that,” Mr Johnson said. “All it will take is a political will to get there.”
Additional reporting by Associated Press
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