The policy would represent a significant shift in how the US manages entry into the country.
In a speech in swing state Ohio today, Trump will also call for "foreign policy realism" and an end to nation-building if elected president.
And he'll argue that the United States needs to work with anyone who shares the mission of destroying the Islamic State group and other extremist organisations, regardless of other disagreements.
The Republican nominee's foreign policy address comes during a rocky stretch for his campaign. He's struggled to stay on message and has consistently overshadowed his policy rollouts, including an economic speech last week, with provocative statements, including falsely declaring that President Barack Obama was the "founder" of the Islamic State.
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Democrat Hillary Clinton has spent the summer hammering Trump as unfit to serve as commander in chief. She's been bolstered by a steady stream of Republican national security experts who argue the billionaire businessman lacks the temperament and knowledge of world affairs to be president.
Trump is expected to say that any country that wants to work with the US to defeat "radical Islamic terrorism" will be a US ally, though aides did not specify which countries that position refers to.
He'll also call for declaring in explicit terms that, like during the Cold War, the US is in an ideological conflict with radical Islam.
"Mr Trump will outline his vision for defeating radical Islamic terrorism, and explain how the policies of Obama-Clinton are responsible for the rise of ISIS and the spread of barbarism that has taken the lives of so many," Miller said Sunday in an email, using an alternative acronym for the Islamic State group.
Under Trump's new immigration policy, the government would use questionnaires, social media, interviews with friends and family or other means to determine if applicants support American values like tolerance and pluralism.
It is unclear how US officials would assess the veracity of responses to the questionnaires or how much manpower it would require to complete such arduous vetting.
The campaign has yet to say whether additional screenings would apply to the millions of tourists who spend billions of dollars visiting the United States each year.
Trump said he will keep that the radical Islamic
terrorists "the hell out" of the country.
"At the same time, we're going to take care of our military and we're going to take care of our great, great, great veterans," he said.
Referring to South China Sea, Trump said the Chinese were building a massive fortress against everything.
"A massive fortress in the South China Sea. Yet they're ripping us off. Now, if they're going to rip us off, you wouldn't think they'd be building fortresses. They have no respect for our President - which I can understand that - they have no respect for Obama, they have no respect for our country, and they're getting away with murder," he said.