A resident, speaking on condition of anonymity, said "at around 5:00 am, unidentified armed men attacked Kati," a town on the edge of capital Bamako where a large military base is located.
"We were woken up at five o'clock by firing, by explosions, we don't know what's going on," another resident said.
A third source said: "Our base is being attacked."
The authorities in Kati could not be immediately reached for comment.
At 8:00 am, an AFP journalist also heard detonations that came from inside the camp.
Malian special forces personnel were deployed in the area, and two helicopters flew overhead.
The French embassy sent text messages to French nationals saying "attack underway at Kati" and urging caution.
The base at Kati has played an important part in military coups.
It was the springboard for mounting the 2020 putsch, and afterwards was used to detain Keita.
In the 2021 coup, the base was used to hold Keita's successor, Bah Ndaw, and prime minister Moctar Ouane.
At dawn on Friday, at about the same time as the gunfire was heard at Kati, suspected jihadists carried out further attacks on security forces, including at Kolokani, about 100 kilometres (60 miles) north of the capital.
In the latest attacks, central Mali and the Koulikoro region near Bamako were hit by six simultaneous assaults on Thursday.
A spat with France has triggered a pullout of French forces that have been fighting jihadists in Mali for nearly a decade. The withdrawal is expected to be completed in the coming weeks.
Tensions, meanwhile, have brewed with the UN's peacekeeping force MINUSMA, whose spokesman this week was told to leave the country.