The interim boss has also guided the Blues to the Champions League final in his short spell in charge, along with improving their disappointing Premier League form.
The 31-year-old has already praised the Italian on Friday for what he has achieved in his two months at Stamford Bridge since Andre Villas-Boas’ sacking, and Terry hopes that silverware can land Di Matteo the role full-time.
“It would do him no harm at all,” the skipper told the club’s official website on Friday.
“He's obviously done very well in the league and all competitions to get us where we are today.
|25/1||John Terry is 25/1 with PaddyPower to score the first goal in the FA Cup final|
“To win it [the FA Cup] will put himself in a very good position.
“He's not thinking of that at the moment, he's not letting the players get distracted by anything.
"He's very passionate, he's Chelsea through and through, and that's certainly rubbed off on the players. So, if we can do it with the added bonus that Robbie can get the job at the end, that'd be great.”
Chelsea face Liverpool in the Wembley showpiece on Saturday, with the crucial European final against Bayern Munich scheduled for May 19.