Burundi has consistently opposed the idea of the AU's proposed 5,000-strong peacekeeping mission, saying the deployment of troops without its express permission would be tantamount to an "invasion force".
The UN has warned Burundi risks a repeat of a 1993-2006 civil war, with hundreds killed since April 2015, when President Pierre Nkurunziza announced he would stand for a controversial third term in office, and at least 230,000 people fleeing to neighbouring countries.
"This is unimaginable," the Senegalese diplomat added.
AU leaders are debating the crisis in Burundi at a two-day summit at the 54-member bloc's headquarters in Ethiopia. Talks are being held behind closed doors and it is unclear when a final decision will be taken.
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Fall said the leaders were considering sending a "high-level delegation, not to say very high" to Burundi to hold talks with the government.
Since his re-election in July, clashes between government loyalists and the opposition have turned increasingly violent.
The AU charter's Article 4 (h) gives the pan-African bloc the right to intervene in a fellow nation state "in respect of grave circumstances, namely: war crimes, genocide and crimes against humanity."
But analysts say other African nations are wary of setting a precedent of deploying troops against the government's wishes.
UN Secretary-General Ban Ki-moon, speaking on Saturday as the AU summit opened, made clear troops were needed to stem the violence.
He said the UN backed the AU's proposal "to deploy human rights observers and to establish a prevention and protection mission".