The Associated Press news agency reported on Thursday that fighters had laid siege to Gbagbo while negotiators continued to try coax him out.
Earlier on Wednesday, negotiations led by the UN and France aimed at securing the departure of Gbagbo had failed according to Alain Juppe, the French foreign minister.
"The negotiations which were carried out for hours yesterday between the entourage of Laurent Gbagbo and Ivorian authorities have failed because of Gbagbo's intransigence," Juppe told the French parliament.
It was not clear if Juppe was simply formally filling them in on earlier events, or if they have tried again to coax Gbagbo out of his bunker.
Earlier in the day, forces loyal to Alassane Ouattara, the president-elect, stormed the residence where Gbagbo is hunkered down.
A spokesman for Ouattara's fighters, Yves Doumbia, said their forces breached the gates of the ruler's compound, only to be repelled by heavy arms fire.
"We retreated but we are preparing for a second assault," Doumbia said.
Patrick Achi, spokesman for Ouattara's parallel government, said troops had been ordered not to kill Gbagbo.
"Alassane Ouattara has given formal instructions that Gbagbo is to be kept alive because we want to bring him to justice," he said.
Issiaka Konate, the UK representative for Ouattara's party, the Rally for Republicans, told Al Jazeera that they have "not captured Gbagbo yet".
"The situation is that he is inside a bunker that has the capacity to house a few hundred people, so we are not sure how many he has with him," he said.
"Gbagbo is still hiding and President Ouattara wants him seized and alive."
The news came hours after Edouard Guillaud, the French armed forces chief, said on Wednesday that Gbagbo's departure would come in "a matter of hours".
South Africa, Togo and Angola are possible safe havens for Gbagbo should he negotiate an exit from his West African country, African Union (AU) sources said on Wednesday.
