Di Matteo, like Grant, took over in mid-season after Russian owner Roman Abramovich had wielded his axe and the former Chelsea midfielder has galvanised the squad, taking them to the FA Cup final and now the Champions League final.
Tuesday's 2-2 draw against Barcelona in the Nou Camp, which sealed a 3-2 aggregate victory in the Champions League semi-final, typified the spirit the London club has displayed since Andre Villas-Boas had his short reign curtailed in early March.
"I think Roberto deserves one more year at least but Abramovich sometimes thinks differently," Grant, whose Chelsea side lost on penalties to Manchester United in the 2008 final in Moscow, told the BBC.
"He has sacked many managers but until now the football was on the way down and the team was on the way down.
"I think in his eyes the team is on the way up and Di Matteo has a chance to continue."
Di Matteo has certainly done his job prospects no harm since taking over from Villas-Boas on an interim basis.
Of the 15 matches since the Portuguese was sacked, Chelsea have lost only one, away to Manchester City.
The players are quick to point out the impact the Italian has had.
"He's created an atmosphere, a spirit and determination. What he's done in bringing it together and getting a result like this, and the results we've had before, is amazing," midfield stalwart Frank Lampard said.
Grant, however, had a word of caution for Di Matteo.
"In my time we got to the final and played unbelievable football and he [Abramovich] decided I would not continue. Sometimes you never know," he said.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.