Mr Fox was speaking in New York, where he was in town to promote the ties between the two countries.
His comments come just days after the Trump administration told Congress it planned to start formal talks with the UK after it leaves the European Union.
The prospects for a new agreement have already faced scepticism.
US President Donald Trump has taken an aggressive “America First” approach to negotiation and the two sides are likely to disagree on issues such as US farm exports and chemical standards.
Read more here