The move could see the UK government act on calls from campaigners to international leaders for a response to the refugee crisis - which is likely to follow the Taliban’s takeover in Afghanistan.
ITV News understands it will be similar to the scheme which brought up to 20,000 Syrian refugees to the UK during the country's decade-long civil war.
Under the current scheme, up to 10,000 Afghans and their families who have worked for the British government are eligible to settle in the UK, but this could be expanded further under the government's expected plans.
However, the fast-developing situation in Afghanistan and the Taliban's lightning rise to power means it is very difficult for Afghans to leave the country, especially those who are not currently in the capital, Kabul.
ITV News understands Home Secretary Priti Patel is keen to prioritise women and girls under the "bespoke humanitarian route".
The UK government has stressed that its first priority is to British nationals.
British armed forces numbers in Afghanistan are to be bolstered to 900 as the push to get UK nationals and selected Afghans out of the country intensified since the Taliban took Kabul.
Nobel Laureate Malala Yousafzai – who was shot in the head by the Taliban in 2012 after enraging them with her campaign for girls' schooling – is the latest high-profile figure to push for all countries to open their borders to Afghan refugees amid the Taliban resurgence.
Speaking ahead of the PM's anticipated announcement, a Downing Street spokesperson said: "The UK team in Afghanistan is working around the clock in incredibly difficult circumstances to help British nationals and as many others as we can get to safety as soon as possible.
"At the same time, we are bringing together the international community to prevent a humanitarian crisis emerging in Afghanistan – it’s in everyone’s interest not to let Afghanistan fail.
"That means providing whatever support we can to the Afghan people who have worked so hard to make the country a better place over the last 20 years and who are now in need of our help."
Watch ITV News Senior International Correspondent John Irvine’s eyewitness report from Kabul where he spoke to a Taliban commander and saw women’s beauty salons shut as the militants took over.
Officials said Mr Johnson was agitating for high-level international discussions on the unfolding crisis, including using the UK’s G7 presidency to call a virtual meeting in the "coming days".
He wants G7 leaders to focus on ensuring Afghanistan does not once again become a source of international terrorist threats, No 10 said.
There will also be an effort to secure support for the people of Afghanistan, including through increased humanitarian assistance and agreeing expectations of whatever government emerges in Afghanistan.
Downing Street wants the five permanent members of the United Nations Security Council (UNSC) – which, as well as the UK, includes the US, China, France and Russia – to meet following the full gathering that took place on Monday.
Following the prime minister’s phone call with French President Emmanuel Macron, in which he raised the prospect of a G7 meeting, the UK and France are expected to work together on a joint UNSC resolution.