It comes as Taliban reached the outskirts of Kabul.
Vice-president Amrullah Saleh is also reported to have fled.
Ghani has come under increasing pressure to resign as major cities around Afghanistan have fallen to Taliban militants over the course of 10 days, reports the BBC.
Meanwhile, footage posted online by a pro-Taliban news agency appears to show inmates being freed from the Pul-e-Charkhi prison in Kabul – the largest prison in Afghanistan.
Earlier on Sunday, Taliban forces overran the military prison at the former Bagram US air base.
Taliban and extremist fighters, including those belonging to the Islamic State, were among the 5,000 inmates being held at the Bagram prison.