Trump has come under heavy criticism for his stance on Muslims which critics have called discriminatory and racist.
But rather than back down from his inflammatory claims, last week Trump doubled down on his call to ban non-American Muslims from entering the United States - even if it causes problems going forward in the general election.
"They're destroying Europe, I'm not going to let that happen to the United States," Trump said during.
While he may be an "exception" to the ban, Khan said today that he is planning to visit the US before this year's presidential elections in November "in case Donald Trump wins".
In an interview with Time magazine, before Trump's announcement, he said: "If Donald Trump becomes the president I'll be stopped from going there by virtue of my faith, which means I can't engage with American mayors and swap ideas."
He has previously expressed admiration for mayors Bill de Blasio in New York and Rahm Emanuel in Chicago, both Democrats, and said he hoped to meet them both.
Khan criticised his rival in the bid to become the next mayor, Conservative party member Zac Goldsmith, for attempting to link him with extremism.
"Conservative [party] tacticians thought those sort of tactics would win London and they were wrong. I'm confident that Donald Trump's approach to politics won't win in America."
Trump became presumptive GOP nominee last week after his chief rival, Ted Cruz, threw in the towel after a disappointing showing in Indiana. John Kasich suspended his campaign the following day.
Generally, in politics, the nominee will shed off some of his positions that are more in line with the party's base in order to be palatable to the general public.
But on the Muslim ban, which is likely Trump's most controversial position, he's not budging.
"I don't care if it hurts me," he told said today. "I'm doing the right thing."
"I've been guided by common sense, by what's right," he continued.
"We have to be careful. We're allowing thousands of people to come into our country," he said. "Thousands and thousands of people being placed all over the country that, frankly, nobody knows who they are."
"We don't know what we're doing," he added.
Trump originally pulled out the idea in the aftermath of the San Bernardino terror attacks in which two Islamic State sympathisers gunned down 14 at an office holiday celebration.
"Donald J Trump is calling for a total and complete shutdown of Muslims entering the United States until our country's representatives can figure out what is going on," a statement from the Trump campaign read.
Trump later clarified that he meant Muslims who weren't citizens of the United States.
Even though Trump was criticised by many Republicans, including rivals like former Florida governor Jeb Bush and former Vice-President Dick Cheney, he stood firm.
While Clinton is not yet her party's presumptive nominee, the former secretary of state's campaign already bashed Trump today on his support of the Muslim ban.
"Trump is going to be the Republican nominee," said a fundraising letter signed by Clinton's deputy communications director Christina Reynolds.
"And if he wins the White House, he could erect a wall on the Mexican border, put women in jail for having abortions, and ban Muslims from coming to our country - and those are just some of the ideas we know about so far," she wrote.
