Eight journalists, including the magazine's editor, and two policemen were among the dead. Police have named the suspects, who include two brothers.
The three suspects have been named in a police document circulated to regional forces as Hamyd Mourad and brothers Said Kouachi and Cherif Kouachi.
Media reports described Cherif Kouachi as a militant sentenced in 2008 to three years in prison for belonging to a group sending jihadist fighters to Iraq.
There are separate reports of police operations taking place outside the capital and in the eastern city of Reims, 140km from Paris, BBC reported.
A large security operation involving elite commandoes is taking place in Reims, although officials are refusing to give any details.
Protests over the attack, the deadliest the country has seen in decades, are being held across France.
President Francois Hollande called it a "cowardly murder" and declared a day of national mourning on Thursday.
He said the country's tradition of free speech had been attacked and called on all French people to stand together. "Our best weapon is our unity," Mr Hollande said in a televised address late on Wednesday.
Security has been stepped up across France in the wake of the attack, with Paris placed on the highest alert.
The satirical weekly has courted controversy in the past with its irreverent take on news and current affairs. It was firebombed in November 2011 a day after it carried a caricature of the Prophet Muhammad.