Mr Gbagbo is sheltering with his family in the basement bunker of his residence in the main city, Abidjan.
Troops loyal to Mr Gbagbo's rival, UN-recognised President Alassane Ouattara, say they have surrounded the compound.
The UN says Mr Gbagbo's military and civilian advisers are leaving him.
Three of his generals - the head of the armed forces, the head of the police and the head of the republican guard - have opened negotiations, the UN told the BBC's Andrew Harding, who is on the outskirts of Abidjan.
'War is over' "We are very close to convincing him to leave power," French Foreign Minister Alain Juppe told the National Assembly in Paris.
Mr Gbagbo's spokesman, Ahoua Don Mello, told the Reuters news agency there were "direct negotiations based on African Union recommendations which said Alassane Ouattara is president".
"They are also negotiating judicial and security conditions for Gbagbo's camp and his relatives," Mr Don Mello said.
Mr Gbagbo has refused to leave office even though the Ivorian election commission declared him the loser of November's run-off vote, and the UN certified the result.
Our correspondent, Andrew Harding, says news of the surrender talks has been circulating rapidly.
It has not been greeted with excitement but with a weary sense of relief, he says, as people ask why Mr Gbagbo had to put them through all this war and destruction.
Mr Gbagbo's army chief, Gen Philippe Mangou, told the AFP news agency his troops had stopped fighting.
"Following the bombardment by the French forces on some of our positions and certain strategic points in the city of Abidjan, we have ourselves stopped fighting and have asked the general commanding [Unoci] for a ceasefire," Gen Mangou said.
UN and French helicopters had attacked several targets on Monday.
Gen Mangou deserted last week, but was said to have returned to the Gbagbo fold on Monday after an apparent change of heart.
Mr Gbagbo's foreign minister, Alcide Djedje speaking from the French embassy in Abidjan, told the BBC the "war is over". As he spoke, shooting could be heard in the background.