But haggis will not be included in the removal of restrictions, as offal products are treated separately from red meat.
Washington last year lifted a ban on beef from the UK, and US president Joe Biden indicated in talks with the prime minister at the White House on Tuesday that lamb was also likely to benefit from the relaxation.
Downing Street said that the final details remain to be worked through, but that a formal agreement should be reached soon.
The move would be some consolation for Mr Johnson, who was forced to accept that his long-cherished dream of a comprehensive post-Brexit free trade agreement with the US was firmly on the back burner.
The UK government is considering the alternative of joining the North American free trade area (USMCA) with the US, Mexico and Canada.
But Mr Johnson’s official spokesperson made clear that this initiative was still at no more than its embryonic stage and was not a current priority.
“What we are focused on is the US deal,” said the spokesperson. “There are no plans to go beyond that at this stage. That is the priority for us.”
Speaking outside the Capitol building in Washington, where he was due to meet leading Democrats and Republicans, Mr Johnson welcomed the expected lifting of the 1996 ban on lamb.
He insisted there was a “great deal” to be made on trade with the US, but accepted that without White House focus on the issue the UK could hope for no more than “incremental” progress.
“I can tell you today that what we’re going to get from the United States now is a lifting of the decades-old ban, totally unjustified, discriminating on British farmers and British lamb,” said the prime minister.
“It’s about time too. And what we’re wanting to do is make solid incremental steps in trade.
“The Biden administration is not doing free trade deals around the world right now, but I’ve got absolutely every confidence that a great deal is there to be done.
“And there are plenty of people in that building behind me who certainly want a deal.”
Mr Biden appeared to catch the PM by surprise at Tuesday’s meeting when he mentioned the potential for the lamb ban to be scrapped.
As Mr Johnson expressed his appreciation for the resumption of beef sales, Mr Biden interrupted to say: “We’re going to be working on lamb too.”
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies