The new Foxes boss has held talks with the midfielder but he is yet to commit his future to the club after his contract expired last month.
Ranieri faced the media for the first time since signing a three-year deal after replacing the axed Nigel Pearson last week and has made keeping Cambiasso a priority.
He managed Cambiasso at Inter Milan between 2011 and 2012 but needs an answer from the former Argentina midfielder.
“I’ve had a conversation with him. I have spoken to him, I know him from Inter Milan, I coached him there. I said to him ‘I need you, everybody loves you in Leicester, please come back’,” said Ranieri, who takes the Foxes to Lincoln for a friendly on Tuesday.
“He told me he wants to wait and look at all the opportunities offered to him and then he will choose. But we need ‘Yes or No’ because at the start of the season he is a team leader and if he doesn’t come I need another team leader. We don’t start the season without a player like him.”
Director of football Jon Rudkin added: “In relation to Esteban, we spoke with him at the end of the season. We’re trying very hard to sign him for the next season. Hopefully in the near future we will get answers one way or another.
“We are very hopeful. He is a world-class footballer who is well sought after.”
Ranieri, whose last job saw him sacked by Greece in November, knows he is under the spotlight after a shock return to the Barclays Premier League.
The Italian, coaching in England for the first time since leaving Chelsea in 2004, said: “In Italy the pressure is everywhere. It’s just the games are when there is no pressure. Before and after the pressure is a lot.
“It’s normal. Everybody wants to win and we are ready to fight. That’s important for me fight in every match and for every ball until the end of the match.”
Chief executive Susan Whelan refused to elaborate why Pearson was sacked last month – with the Foxes citing a breakdown in relationship with the board – but insisted it was for the good of the club.
“The club is a better place for the contribution that Nigel has made in the past. However for the pursuit of the long-term objectives and vision for this club of the owners, a change was necessary,” she said.
“I am very confident in Claudio we’ve recruited a manager who has the knowledge, the passion and the determination to ensure the continued growth and development of this club and to fulfil the vision of the owners and everything that is in the hearts and dreams of all of the fans in this club.”
Ranieri also confirmed Pearson’s backroom staff Craig Shakespeare and Steve Walsh will stay at the club.