Since the hardline Islamist group seized the capital city Kabul earlier this week, thousands have sought to leave the country.
The UK government has committed to providing asylum for up to 20,000 refugees seeking safety - and Fife Council's co-leaders say the Kingdom is willing to help out.
In a joint statement, Councillors David Alexander and Cllr. David Ross said: "Fife has always played a lead role in welcoming refugees from around the world, and we stand ready to play our part again.
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"Prior to this unfolding crisis, Fife had already committed to resettle 10 Afghan families.
"We're currently working with other council services and partners including, health, voluntary sector and Police Scotland to see if we can accommodate more families.
"We will be liaising with CoSLA and the Home Office over the next few days to firm up our plans to help Afghan refugees."
The Taliban seized Kabul on Sunday after a 10-day national offensive - the culmination of a months-long campaign that began when the United States commenced the withdrawal troops earlier this year. UK troops remain on the ground in Afghanistan to assist British citizens with repatriation.
Home secretary Priti Patel said of the relocation scheme: "I want to ensure that as a nation we do everything possible to provide support to the most vulnerable fleeing Afghanistan so they can start a new life in safety in the UK
"Our country has a proud history of offering sanctuary to those in need.“