Grant, who was sacked by Chelsea owner Roman Abramovich after losing the 2008 Champions League final to Manchester United in a penalty shoot-out, believes Di Matteo has done enough to earn a new deal.
"Roberto deserves one more year, at least, because he has done a good job with this team. To come to the final with this team is unbelievable," Grant said in the Evening Standard.
However, Grant - now in charge of Serbian club Partizan Belgrade - warned that it would be difficult to predict Abramovich's next move.
"Abramovich sometimes thinks different," he said.
"In my time we came to the first final in the history of the club. We also played unbelievable football in the (Premier) League, in my opinion, beating all the big teams. But then he decided that I would not continue."
But Grant believes Di Matteo has a chance of taking the job on a permanent basis because he has done so much to improve Chelsea's fortunes since replacing the sacked Andre Villas-Boas.
"In this case, Abramovich has seen that the team was on the way up and I think Di Matteo will have a chance to continue," he said.
"For a manager, against Barcelona is the most difficult game you can play. Especially as Chelsea are not great this season.
"But over the two games Di Matteo did a very good job. What is the weakness of Chelsea? Chelsea are not playing great football this season so he went for the strengths of his team, the old players in combination with good tactics, to stop Barcelona."
Source: PA
Source: PA