The president added he did not see any Democrat who could beat him: "I don't see anybody".
Trump, who became the 13 USA president the Queen has met during her 66 year reign, visited the British monarch at Windsor Castle in the English county of Berkshire following his meeting with Prime Minister Theresa May.
Asked if he discussed Brexit with the Queen, Trump said: "I did".
"Everyone thought it was going to be 'Oh it's simple, we join or don't join, or let's see what happens'".
Trump and the 92-year-old monarch shared a few interactions on Friday as they reviewed troops at the royal castle in Windsor.
America's First Lady is an handsome, elegant woman with impeccable taste and style. Just "Welcome". Just very elegant.
The two exhibited strong chemistry, and May said Trump had agreed to "pursue an ambitious US-UK free trade agreement" once Brexit (the UK's withdrawal from the European Union) takes effect on March 29, 2019. "He would be wise not to attempt to kiss her, and I don't expect for a moment that he will". Prime Minister Theresa May, who greeted the Queen with a very low curtsy last time they met in public, backs out of the room after her weekly audience with the monarch - as all British prime ministers have before her.
He said: "I was walking up and I was saying (to Melania) 'Can you imagine my mother seeing this scene?"
A January 2017 report in The Sunday Times newspaper said Trump and Charles would not meet during his visit to Britain due to their strongly divergent views on climate change.
Trump replied: "I think I could have".
"Whatever we think of President Trump, he is the elected president of the United States of America and he has been invited to this country and he must be treated with great civility", Vickers said. "I mean, what are we doing?"
The Royal band played the national anthem of the United States.
Spearheading the group is Former Vice President Joe Biden, who has used his vast political network and decades of experience to reassert himself as a party leader and a vocal critic of Trump's agenda.
Yesterday, a 20-foot-tall "Trump Baby" blimp was flown above Parliament Square with Trump responding to the inflatable and saying it made him feel "unwelcome" in London. He told Mr Morgan: 'I get along with him great, yeah. "Now when people come in illegally they have their kids, there are consequences to that, but I still didn't like the idea of separation".
- Trump Waves at Protestors Calling Him Racist While Golfing in Scotland
- 11 times Donald Trump praised Vladimir Putin
- Kate Middleton and Prince William Release Prince Louis's 3 Official Christening Photos
- Southgate promises strong XI as England target World Cup medals
- Twitter Loves Emmanuel Macron's Excited Reactions During World Cup Final
- Obama in Kenya for launch of sister’s sports center
- Sarri confirmed as new Chelsea manager
- Woman survives for a week after crashing vehicle off 200-foot cliff
- Can Manchester United win the Premier League this season?
- Trump tweets ‘very nice note’ he received from Kim Jong Un