Ranieri was sacked in 2004 after his side were beaten by Monaco in the Champions League semi-final and while goals from Didier Drogba and Frank Lampard put Chelsea into the final, he is unsure that owner Roman Abramovich will be happy with just that.
"I think Grant deserved this victory," the Italian told BBC Radio Five Live.
However, asked what will happen if Chelsea fail to win in the final, the Italian said: "This is a difficult answer but I think if Grant doesn't win, I think he's finished in the job.
"I think if Grant wins something, then okay, maybe he'll continue, but if not ... I don't know the mind of Roman Abramovich, it's very difficult to know what he thinks.
"It is the first (European Cup) final of Chelsea's history, going to Moscow, it's fantastic for him. He'll be very, very proud."
Grant is putting Chelsea to one side today as he will fly to Poland to visit Auschwitz out of respect for Holocaust Day, which took place yesterday.
He collapsed to his knees on the pitch at the final whistle and revealed: "It was a special day for me. Hard but very special. My father buried my grandfather with his own hands, so this day always has an extra significance.
"My father was the most optimistic and strong person I have ever known, so to reach the Champions League Final today of all days was unbelievable."
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