Forces loyal to Alassane Ouattara, president of the country's internationally recognized, say they have built up after days of fierce fighting.
A spokesman for Mr Ouattara, Patrick Achi, told the BBC it is not yet clear if Mr Gbagbo was in deep.
Earlier, the UN and French helicopters attacked targets near the residence.
UN Secretary General Ban Ki-moon said the attack was ordered to defend civilians and no declaration of war against Mr. Gbagbo.
He said the troops Mr Gbagbo has been increasing use of mortars, rocket-propelled grenades and heavy machine guns against civilians.
Millions of civilians have been trapped by five days of fighting in the city, where Mr Gbagbo refused to leave office despite the outcome of UN-approved says Mr Ouattara won the presidential election in November.
Forces loyal to Mr Ouattara initiate dramatic military attack last week, swept in from the north and west. 'Still looking'
Patrick Achi, a spokesman for Mr Ouattara, have said the president recognized that is controlling the lives and looking for Mr. Gbagbo. Continue reading the main story Ivory Coast: Battle for Power
"Lodging is at various levels," he told the BBC.
"People have seen that Gbagbo was in residence, but they are still looking for him."
When asked what would happen if Mr Gbagbo was arrested, he said he would be arrested and "taken to court."
No word from the camp Mr Gbagbo in Ivory Coast but one of the advisers in London, George Abdon Bayeto, expressed doubts about the story residence has fallen.
"This is all propaganda and it's all psychological warfare," he said.
Earlier, the UN and French helicopters attacked Mr Gbagbo's arsenal, missile firing heavy weapons and military camps.
A senior official of peace, Alain Le Roy, said the decision was based on UN Security Council resolution expressly permit the Board of such action to protect civilians.
The use and heavy caliber weapons by force Gbagbo has, he said, increased sharply in recent days.
The UN mission has been under almost constant attack and have been forced to act, he said.
However, air strikes to coincide with what looks like the final attack on Mr Gbagbo's last stronghold by troops loyal to rival Mr Ouattara, the BBC's Barbara Plett reports from the UN in New York.
Analysts say the timing is not likely a coincidence because there is a feeling that the month-long stand-off between the two claimants president was nearing an end.
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