Brunel, who succeeded Nick Mallet as head coach after last year's World Cup, made the bold claim despite the Azzurri having never finished in the top half of the championship standings.
Speaking at the official Six Nations launch in London, the 58-year-old said: "Every year, we come back here and think, who's going to win the championship?
"Is it going to be France, is it going to be England? How are they going to play? Who's going to win it in the end?
"What I hope now is that in two years time, you will all come back here and you would say to me, what if it Italy was to win the championship?"
Italy have steadily improved since joining the competition in 2000 and last season secured a landmark victory against France, who they face in next weekend's tournament opener.
Captain Sergio Parisse targeted an even bigger scalp in the shape of England the following week.
"The France victory gave us the confidence to say to ourselves that we are able to beat this team," he said.
"The first match at home is against England, so for us it's a big challenge, big responsibility.
"We are really excited to play this match.
"Every time we are at home, we must win."
But number eight Parisse insisted beating England was less important to Italy's progress than ensuring they perform in every match.
"I don't know if we're going to progress more if we beat England and lose the other matches," he said.
"If we can play every match of the Six Nations and we're close to winning every match, that is very good progress.
"If we just have a good victory and the match after we lose by 30 or 40 points, it's still the same."