By making it clear Ms Truss does not believe a trade deal is likely, the Government believes this will lessen the impact of any US threats.
President Biden has shown no interest in starting trade talks with Britain or any other major country in his first two years in office, the source said.
It had been planned that the two would meet in Downing Street at the weekend, but the meeting was postponed until Wednesday – a decision seen by some as a snub.
She told reporters on the plane to New York that she was concentrating on reaching trade deals with India and countries in the Pacific.
Asked about the meeting with President Biden, Ms Truss said: “The number one issue is global security and making sure that we are able to collectively deal with Russian aggression and ensuring that Ukraine prevails and that Putin doesn’t have success in Ukraine.
“That is a huge priority for European security as well as ensuring that we are working together with other members of the G7 to make sure we are not strategically dependent on authoritarian regimes.”
Truss turns focus to India trade deal
Ms Truss said her priorities were to join the Comprehensive and Progressive Agreement for Trans-Pacific Partnership (CPTPP), a trade agreement bringing together Australia, Canada, Japan, Mexico, New Zealand and six other countries.
She also said she wanted to reach an agreement with the Gulf Cooperation Council of Arab states.
“In terms of trade: I mentioned earlier getting CPTPP accession, getting a trade deal with India, getting a trade deal with the GCC,” she said. “Those are our trade priorities.
“There isn’t currently any negotiations taking place with the US and I don’t have an expectation that those are going to start in the short to medium term.”