Four suspected suicide blasts hit the Mulaikalmari and Sabon Gari areas of the city in quick successions, the source said, Xinhua reported.
Eight people, including two suicide bombers, died in the first and second attacks while three more people were killed in the following attacks.
Five people were injured, according to eyewitnesses.
Head of the government emergency agency Satomi Ahmed, while also confirming the attacks, said rescue operation was still ongoing in the areas.
A senior security agent suspected that the attacks were carried out by Boko Haram.
The security officer said the terror group had attempted to infiltrate Maiduguri, the Borno State capital, after they were chased out of the city.
Boko Haram has been blamed for the deaths of more than 20,000 people and displacing of 2.3 million others in Nigeria since their insurgency started in 2009.