It follows worries that Britain's "special relationship" with the US had cooled.
Mr Mnuchin said Britain would still be at the "front of the queue" for a bilateral free trade deal following the exit from the European Union.
"As soon as the UK is ready we will be prepared to negotiate an attractive trade deal," he told the BBC in Davos.
I asked Mr Mnuchin if the relationship between the US and Britain had become strained after President Donald Trump cancelled a meeting to come to the UK to open the new US embassy in London.
President Trump also criticised Prime Minister Theresa May on Twitter after clashing over his retweet of Britain First videos.
Mr Mnuchin said that a positive economic future for Britain was very important to the US, and that America was maintaining full support for the UK over "the Brexit issue".
He said the US administration was "monitoring the discussions", adding: "We want to see a successful transition."
Mr Mnuchin met Mark Carney, Governor of the Bank of England, on Wednesday to discuss Brexit, and he will meet Philip Hammond, the chancellor, later on Thursday.
The US Commerce Secretary, Wilbur Ross, said that he had met the British international trade secretary, Dr Liam Fox, to discuss stronger trade relationships.
He said the UK would be following the US model of having "commercial officers" based in every embassy to boost economic and business ties.
Source: BBC News