Cambiasso, who played a crucial role in keeping the Foxes in the Premier League last season, announced last week he would not be renewing his contract with the club having joined in August 2014 on a one-year contract from Inter Milan.
Although he refused to disclose the name of the player, Ranieri revealed he is hopeful of completing a deal to sign a midfielder to fill the void left by the former Argentina international.
“We are still looking. We are very close with a good player,” the Leicester boss said following his side’s 2-1 pre-season victory over Burton on Tuesday.
When asked about the challenge of replacing Cambiasso, Ranieri added: “Yes, of course, because Esteban is a good player, a leader and it is difficult to replace him. But we are looking for him.
“We are very close (with a replacement). But I wait until the end of the window.”