Home Affairs Minister Mwigulu Nchemba said today that over 8,000 refugees are "pushing to be returned" after they registered for voluntary repatriation.
UNHCR in Tanzania did not respond to a request for comment.
In July, Tanzanian President John Magufuli suspended the registration and naturalization of thousands of Burundian refugees.
Over 240,000 Burundians are sheltering in Tanzania after fleeing deadly political violence.
Burundian President Pierre Nkurunziza recently urged the refugees to return, saying the country is now peaceful.