The Republican presidential front-runner made the comment after addressing high school students here at their homecoming Saturday night.
During a question-and-answer session with students, Trump was unable to avoid being asked about the latest political controversy dogging his campaign: his decision not to correct a supporter this week who called President Barack Obama a Muslim.
One student told Trump that she considered Muslim-Americans to be an important segment of the country. They asked whether the billionaire businessman would consider putting a Muslim in his Cabinet or on his ticket.
"Oh, absolutely," Trump responded. "No problem with that."
Trump also told CNN's Jake Tapper on "State of the Union" he has friends who are Muslims -- but that the religion's extreme elements are responsible for terrorist attacks.
"We do have a problem with radical Muslims, there's no question about that," Trump said Sunday.
At a New Hampshire town hall on Thursday
, a supporter stated that Obama was a Muslim and not American -- which Trump did not correct -- and asked the candidate how he plans to "get rid of" Muslim "training camps" in the country.
"We're going to be looking at a lot of different things," Trump responded. "You know, a lot of people are saying that and a lot of people are saying that bad things are happening."
Trump has largely avoided the press since the flap. He canceled a South Carolina campaign event on Friday, citing business obligations, and chose to forego press gaggles at two events in Iowa on Saturday.
Under fire from critics for the interaction, Trump sent out a series of tweets
Saturday, defending why he chose not to correct the supporter.
"Am I morally obligated to defend the president every time somebody says something bad or controversial about him? I don't think so!" Trump wrote.
In another tweet, he said: "If I would have challenged the man, the media would have accused me of interfering with that man's right of free speech. A no win situation!"
Trump was noticeably subdued as he addressed a crowd of teenagers ahead of their dance on Saturday, advising them to stay away from alcohol and drugs and encouraging them to pursue professions they felt passionate about.
Taylor Donner, a senior at Urbandale High School who attended Trump's speech wearing his tux and boutonniere, was excited to see the candidate.
"I'm a fan. I didn't think we'd get someone that important," he said. Donner spoke to CNN while his homecoming date, Raelynn Meade, got to meet the real estate mogul because she was part of the AP government class that helped get him here.
Not every Urbandale student is a Trump fan, though. According to Donner, his friends are supporting different candidates, including Vermont Sen. Bernie Sanders. One of those friends is Josh Ingham who wore his "Feel The Bern 2016" shirt and pin to the speech.