The national team will have a new skipper for this summer's European Championship following the controversial decision to relieve John Terry of the armband last week, which ultimately led to Fabio Capello's departure as England boss.
Liverpool talisman Steven Gerrard and Tottenham's Scott Parker are thought to be among the favourites but Mancini thinks in-form City midfielder Barry is an excellent candidate. The Italian said: "He could be [captain] because he is a good man, a clever man on and off the pitch. He is a really good player."
He added: "For me, like for Capello, he should play always for the national team because he is a very intelligent man.
"He has played a lot of games for the national team but I think there are two or three players who could be captain."
Barry, 30, has become an England regular in the past four seasons and now has 51 caps to his name.
Mancini has been impressed with his performances at club level this season, feeling the former Aston Villa player has had a key role in City's Barclays Premier League title challenge.
Mancini said: "Gareth is a strange player.
"In every team there are some players who seem not important but, in the end, they are the most important players.
"These players are quiet but they can play in every position, they help the manager, their team-mates. They are always available and fight for every ball. Gareth is a player like this. He is really important."