Ranieri had been at the helm for just a few weeks when Di Matteo suffered a broken leg away at St Gallen, an injury which ended his career.
The midfielder tried to come back but to no avail and it was during that time that Ranieri saw the characteristics which appear to have helped Di Matteo become a good manager.
He told the London Evening Standard: “He was with the medical staff all the time, it was a very hard time, but you could see his character and his determination to come back.
“I could tell he had the skills you need to be a manager. Could he get the job now? Why not? He is working very well now.
“If Chelsea win the FA Cup, finish in fourth position in the League and win the Champions League, he deserves to continue. I wish for him that he gets the job.”