The report by the UN's Office for the Coordination for Humanitarian Affairs (OCHA) put the daily arrivals rate at 774 and said it expected 30,000 refugees to arrive in the country this year.
"The humanitarian community believes that an additional population influx is expected given the security context -- the increase in attacks by Boko Haram in northern Nigeria as well as possible tensions before elections," the report said.
Nigerians go to the polls on February 14 with President Goodluck Jonathan looking to secure a second four-year term.
On Sunday, Boko Haram insurgents took control of the city of Monguno and its military base close to Lake Chad in northeast Nigeria after intense fighting with the Nigerian army.
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Chad has called on countries in the region to form a broad coalition in the fight against the Islamist group. The country has already deployed its army along its borders and is sending an additional contingent to Cameroon.
Chad's president Idriss Deby has also expressed intentions of taking back the strategic Nigerian town of Baga from Boko Haram, situated on Lake Chad.