Ranieri is hopeful the experienced midfielder will sign a new deal but says the club need to know either way so they can make contingency plans if required.
Ranieri has signed a three-year deal at Leicester after replacing Nigel Pearson as boss and has made a new contract for Cambiasso one of his top priorities.
The 34-year-old Argentine midfielder was a key figure at Leicester last season as they secured Premier League survival but his contract expired last month.
Cambiasso has worked under Ranieri before and has already held talks with the new Foxes boss but he has yet to commit himself to the club.
Ranieri said: “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’.
“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 says Leicester are optimistic about getting a deal done but are aware that Cambiasso is likely to receive other offers.
“In relation to Esteban, we spoke with him at the end of the season,” said Rudkin. “He is a world-class footballer who is well sought after.
“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.”