In an interview with the Financial Times, May said: "I'm also confident the USA will recognise the importance of the cooperation we have in Europe to ensure our collective defence and collective security."
The British premier is expected to visit Trump in the spring, according to Downing Street, although the FT reported that she could go to Washington as early as next month.
Earlier this week, before he was sworn in as president, Trump told two European newspapers he had long warned that NATO had "problems".
"Number two, the countries aren't paying what they're supposed to pay."
In his inaugural address today, Trump said the United States had "subsidised the armies of other countries", highlighting a common course of friction in the 28-nation alliance.
In response to Trump's reported remarks about NATO earlier in the week, German Chancellor Angela Merkel warned Europe has to take responsibility for itself.