Mr Johnson instead talked up the chances of close co-operation with the Biden administration on climate change, as Britain prepares to host the crucial COP26 international summit in 2021.
While outgoing president Donald Trump was an enthusiast for a post-Brexit trade deal with the UK, Mr Biden has been more circumspect, signalling that it will be off the table if the process of Britain leaving the EU puts peace in Northern Ireland at risk.
And an unnamed foreign policy adviser to the Biden campaign told the Daily Telegraph that trade talks with Britain would not be a priority in the new president’s first 100 days in office, when he is expected to concentrate on coronavirus, economic recovery, immigration reform, infrastructure and climate change.
Speaking in public for the first time since Mr Biden’s victory over Mr Trump in the presidential election, the normally bullish prime minister stopped well short of saying that a deal would be done.
“On the trade deal with the US, I’m a keen student of the United States’ trade policy and they’re tough negotiatiors,” he told the AP news agency.
“And I’ve never believed that this was going to be something that was going to be a complete pushover under any US administration.
“I think there’s a good chance we’ll do something. (International trade secretary) Liz Truss and her team have made a huge amount of progress and we’ll get on.”
The prime minister has previously hailed an agreement with the US as one of the biggest supposed prizes from Brexit, and in early 2017 said that Britain was “first in line to do a great free trade deal” with the Trump administration.
Mr Johnson indicated that he intends to press ahead with legislation designed to allow UK ministers to override the Northern Ireland protocol he signed with the EU last year in a way which the government admits will break international law.
Mr Biden was one of many to respond with horror to the Internal Market Bill, warning: “We can’t allow the Good Friday Agreement that brought peace to Northern Ireland to become a casualty of Brexit. Any trade deal between the US and UK must be contingent upon respect for the Agreement and preventing the return of a hard border. Period.”
Provisions relating to Northern Ireland are expected to be struck out by peers as the bill returns to the House of Lords next week. And the European Parliament has made clear it will not ratify a UK/EU trade deal if the bill becomes law without the removal of the measures.
Asked if he intended to ensure the legislation passes through parliament “as it is”, Mr Johnson replied: “Yes.”
The PM said he had told European Commission president Ursula von der Leyen in a phone call yesterday that “the parliamentary timetable goes ahead” on the bill.
He said: “The whole point of that bill, and indeed the Finance Bill, is to protect and uphold the Good Friday Agreement and the peace process in Northern Ireland. And again, that’s one of the things that we’re united on with our friends in the White House.”
Mr Johnson said he had not yet spoken to Mr Biden or vice president-elect Kamala Harris since the election result was called on Saturday, but said he wanted to congratulate them on their victory.
He brushed aside Mr Biden’s previous description of him as “a physical and emotional clone of Trump”.
“The United States is our closest and most important ally, and that’s been the case under president after president, prime minister after prime minister,” said Mr Johnson. “It won’t change.
“I look forward to working with President Biden and his team on a lot of crucial stuff for us in the weeks and months ahead – tackling climate change, trade, international security and many, many, many, many, many other issues.
“I think that there is far more that unites the government of this country and government in Washington any time, any stage, than divides us.
“We have common values. We have common interests. We have a common global perspective.
“There’s a huge amount of work we need to do together to protect those values – a belief in democracy, in free speech around the world, in human rights, in free trade, in the rules-based international order.
“All of these things are currently under threat. And you have the United States and Britain standing together, as they have done many times in the past, to protect those values. So I think there’s far more that that unites us than divides us.”
MrJohnson said he was hopeful that a Biden presidency would improve the chances of global agreement on net zero carbon emissions by 2050 at the COP26 climate change summit being hosted by the UK in Glasgow next year.
“Already you’ve got country after country lining up to support the ambition of net zero by 2050,” he said.
“Japan came through, Korea came through, even China has come through with a plan to do it by 2060, which is absolutely fantastic for the world.
“And I think now with President Biden in the White House in Washington, we have the real prospect of American global leadership in tackling climate change.
“The UK was the first major country to set out that objective of net zero by 2050. We led the way a few years ago. And we’re really hopeful now that President Biden will follow and will help us to deliver a really good outcome of the COP26 summit next year in Glasgow.”