Gunfire was heard near the apartment block in the city of Toulouse, with reports police had met resistance but that the suspect was now dead.
The siege of the building where Mohammed Merah, 23, is holed up has lasted more than a day.
Interior Minister Claude Gueant had said Merah wanted to die "gun in hand" and there was no contact overnight.
It was not certain he was alive, Mr Gueant said.
Agence France-Presse quoted police sources as saying that officers were moving step-by-step through the flat, wary of booby-traps, and as yet there was no sign of Merah.
Mr Gueant earlier told French radio: "We have one priority: to take him alive so that he can surrender to face justice. We hope he is still alive."
However, he said it was "quite strange that he did not react" to the explosions that were set off overnight to intimidate Merah.
"We heard two shots, we don't know what they were," Mr Gueant said.
"Despite redoubled efforts throughout the night, there has been no contact with him."
A number of explosions, beginning late on Wednesday, had prompted deputy mayor Jean-Pierre Havrin to tell local media that "negotiations have finished and the assault has begun".
However, sources from the French interior ministry later said this was only the start of an operation to put pressure on Merah.
"[The blasts] were moves to intimidate the gunman, who seems to have changed his mind and does not want to surrender," interior ministry spokesman Pierre-Henry Brandet told Reuters.
Merah had given conflicting messages about surrendering.
Anti-terror chief Francois Molins had said: "He's explained that he's not suicidal, he doesn't have the soul of a martyr and he prefers to kill but to stay alive himself."
Officials said Merah was armed with a Kalashnikov high-velocity rifle, a mini-Uzi 9mm machine pistol, several handguns and possibly grenades.
Street lights were switched off in the vicinity of the building on Wednesday evening.
The five-storey block of flats has been evacuated, and police also moved residents from nearby buildings.
Police had surrounded Merah's building after two officers were shot at when they tried to get into his flat early on Wednesday morning.
Elsewhere in the city, police are hunting for accomplices and have detained several members of Merah's family.
Mr Molins said on Wednesday that Merah had planned to kill again.
"If he's telling the truth, he would have left his house this morning and he would have once again killed any soldier that he came across," he said.
Mr Molins said the suspect had expressed no regret for the killings, but had said he wanted to kill more people and "bring France to its knees".
Merah has said he acted to "avenge Palestinian children".
He claimed to have received al-Qaeda training in Pakistan's Waziristan area, and also said he had been to Afghanistan.
Mr Gueant defended intelligence services for not preventing the attacks, describing Merah as a "lone wolf".
"The domestic intelligence agency tracks a lot of people who are involved in Islamist radicalism. Expressing ideas... is not enough to bring someone before justice," Mr Gueant said.
Christian Etelin, a lawyer who has previously acted for Merah, said his client had violent tendencies.
"There was his religious engagement, an increasing hatred against the values of a democratic society and a desire to impose what he believes is truth," Mr Etelin said.
He also denied earlier reports that Merah had been jailed for explosives offensives in Afghanistan, saying his client was in jail in France for robbery with violence at the time - from December 2007 to September 2009.
The killings took place in and around Toulouse in three separate incidents earlier this month.
On 11 March, a soldier was shot and killed while waiting to see a man about selling his motorcycle.
Days later, two soldiers were shot and killed and a third was wounded while waiting at a cash machine.
Then earlier this week, three children and an adult were shot and killed outside a Jewish school.
The four Jewish victims were buried in an emotional funeral in Jerusalem on Wednesday.
Also on Wednesday, President Nicolas Sarkozy attended a memorial for the three murdered soldiers at a military base in Montauban near Toulouse.
The siege of a gunman suspected of seven killings in southern France is nearing its end, police sources say.