Judges ruled on Tuesday that prosecutors had failed to prove any case against Gbagbo and co-defendant Charles Ble Goude and that his continued detention could no longer be justified. Gbagbo has been in custody for seven years.
"My father will not live in any other country than Ivory Coast. He would go back and we expect him to go back," his daughter, Marie Laurence Gbagbo, told Reuters in an interview outside the court in The Hague.
Her comments came as prosecutors and defence lawyers argued over the terms of his release, a matter judges were due to rule on later on Wednesday. Discussions were continuing with ICC member states about his transfer.
The prosecutors asked the court during procedural hearings on Wednesday morning to bar Gbagbo from returning to Ivory Coast, the world's largest cocoa exporter, saying he would probably not return in the event of an appeal or retrial.
Marie Laurence Gbagbo declined to comment on the former president's possible political ambitions, saying: "I can't speak for my father on this. It is a very delicate question."
Gbagbo's acquittal was deplored by victims' groups for those who died in violence that killed around 3,000 people during Ivory Coast's 2010 elections, which Gbagbo refused to concede.
Hundreds of thousands fled the unrest that prosecutors blamed on Gbagbo and victims fear his return home could revive hostilities in Abijan.
"The defendant's release may increase tensions," Paolina Massidda, a legal representative of the victims, said at the court in The Hague.
Gbagbo's lawyers said the prosecution request showed they had not yet come to terms with the scale of their legal defeat.
"Laurent Gbagbo is no longer an accused person. Laurent Gbagbo has been acquitted. He is no longer presumed to be innocent - he has been acknowledged as being innocent," Gbagbo's lawyer Emmanuel Altit told the court.
"At stake, your honours, is the natural right to freedom, the freedom of mankind. This is the essence of the debate today. Not procedures," defence lawyer Geert-Jan Knoops told the judges. "These two individuals have been acquitted." (Reporting by Toby Sterling; Writing by Anthony Deutsch; Editing by Gareth Jones)