The US President-elect will sign orders next week in a bid to strengthen US borders.
In addition to possible travel restrictions on EU citizens, orders could include “extreme vetting” for those from countries known for Islamist terrorism.
Trump’s comments came in his first UK interview as president-elect.
He used the interview to congratulate the UK on Brexit, which he labelled a “great thing”.
Trump said: “People, countries want their own identity and the UK wanted its own identity.
“I love the UK. We’re gonna work very hard to get it [a trade deal] done quickly and done properly. Good for both sides.
“I will be meeting with [Mrs May]. She’s requesting a meeting and we’ll have a meeting right after I get into the White House and it’ll be, I think we’re gonna get something done very quickly.”
But his optimism stopped short when it came to discussing the EU.
The President-elect took a swipe at Angela Merkel over the German Chancellor’s refugee policy.
He said: ”I think she made one very catastrophic mistake and that was taking all of these illegals, you know, taking all of the people from wherever they come from.
”And nobody even knows where they come from. So I think she made a catastrophic mistake, very bad mistake.”
Trump labelled the EU a “vehicle for Germany” and predicted other countries will follow the lead of the UK to leave the Union.
He said: “I believe others will leave.
“I do think keeping it together is not going to be as easy as a lot of people think.
“If refugees keep pouring into different parts of Europe… it’s going to be very hard to keep it together because people are angry about it.”
The President-elect indicated the Berlin terror attack at a Christmas market in December was a consequence of Germany’s open-door policy.
He claimed his relationship with Merkel “may not last long at all” as he slammed the German Chancellor for allowing the migrant crisis to get out of control.