Ranieri was shown the door in February, just nine months after leading them to the Premier League title, with the Foxes perilously close to the relegation zone and in the midst of a woeful run of form.
The club turned to assistant Craig Shakespeare who has gone on to win his first four Premier League games in charge becoming only the fifth ever manager to achieve the feat.
However, Dutchman Hiddink claims it could have all been different despite himself suggesting Shakespeare as a sensible option.
The Dutchman told the Sunday Times: "To be strictly correct, I didn't talk directly with Leicester. But you know how the line goes. 'They think of you...'
"They asked not directly but indirectly, but I said no. If you have decided to sack Ranieri, why don't you go with your number two guy?
"Shakespeare knows the club, knows the players. Why don't you go there, you will see what will happen, I said. Happily I was right.
"Liverpool [Shakespeare's first game in charge] didn't know what hit them. Within 20 minutes, 2-0. And five days later Leicester won at Hull. The relegation problem was solved in five days."