Asked to give an estimated number after a Cabinet Office Briefing Rooms meeting, Raab told reporters the government is currently working it out.
“We’re obviously a big-hearted nation, we’ve got the criteria for asylum that is set in law,” he said.
“We work with the U.N. on that. We’re working very carefully at what kind of further commitment we might make.”
Raab told reporters that everyone has been “surprised by the scale and the pace at which the Taliban have taken over in Afghanistan” and that it’s “a lesson that we’ve all got to learn from.”
He added that the focus right now should be on evacuating British nationals and their Afghan allies out of the country.
Earlier on Monday, Defence Secretary Ben Wallace told Sky News that he suspects there will be “significant migrant flows around the world,” adding that Turkey is already dealing with “significant inflows.”
Suhail Shaheen, spokesman for the Taliban told the BBC on Sunday that it would not retaliate against people who worked for Western forces, but his promises were met with deep scepticism, as many have reportedly received threats.
Wallace said the political leadership of the Taliban does recognise the “lesson of 2011” that hosting terrorists and running a state as they did led to rampant poverty, migration, a refugee crisis, and the toppling of the regime; thus “the onus is on them” to keep their promises.
Wallace said the UK is working with its allies in the region—including Qatar and Turkey—to stabilise the situation.
Tobias Ellwood, chair of the Defence Committee, said that the number is likely to be at least in the “tens of thousands.”
“Because of our departure from Afghanistan, we’re now prompting a massive migration crisis, which requires us to review our policy on receiving asylum seekers from Afghanistan,” Ellwood, a former soldier who previously held ministerial positions in the Foreign Office and the Ministry of Defence, told PoliticsHome.
“In noting what Canada and Germany have done, all NATO countries who participated in Afghanistan need to work together to coordinate efforts in order to facilitate [the] arrival of what will be hundreds of thousands of families fleeing the country.”
Ellwood said he would expect at least “tens of thousands” to enter the UK, but added the UK wouldn’t want to drag itself into a “bidding war” for Afghan refugees by specifying a number too quickly.
“All the countries that were involved have a duty and an obligation to provide safe haven, given where we’ve left the country,” he said.
The UK is currently scrambling to evacuate British citizens and eligible Afghan nations from Afghanistan.
Wallace said there are also “a significant number” of Afghans who managed to get out of the country over the last few weeks and are in refugee camps around the world.
“We’re going to be processing them wherever they are, and we’re going to continue to do that after we’ve gone … we will do everything we can to bring as many people as possible,” Wallace said.