Gesturing to the bust he said: "This is the orginal in many, many ways."
May said "Thank you very much Mr President" and the two leaders then shook hands.
May said the special relationship would be "renewed for a new age" as she became the first world leader to meet Trump since his inauguration.
The White House said Trump and May would hold talks, followed by a press conference and a working lunch.
Kellyanne Conway, counselor to the president, said the UK was America's "premier ally" and the people of the two counties had delivered a "very similar message" through Brexit and the election of Trump.
Conway said: "These are two individuals - two freshly minted world leaders - who came into office very similarly through the people.
"People sent a very clear and convincing message in the US and the UK that they wanted to go outside of the establishment."
In a rare tweet May chose to issue a clip from her speech in Philadelphia yesterday in which she said: "As we rediscover our confidence as you renew your nation just as we renew ours.
"We have the opportunity, indeed the responsibility, to renew the special relationship for this new age.
"We have the opportunity to lead together again because the world is passing through a period of change.
"And in response to that change we can either be passive bystanders or take the opportunity once more to lead, and to lead together."