And the former City midfielder, who announced his retirement last week, hopes to play his part as he begins a new off-field role at the Etihad Stadium.
The wealth of Sheikh Mansour bin Zayed Al Nahyan has elevated City to elite level and last season's FA Cup win will be followed by Champions League participation and a possible title challenge next term.
Vieira, now the club's football development executive, is excited by the possibilities.
The 35-year-old said: "I think the target and the ambition of all the people working for this football club is really high.
"They want to challenge the biggest clubs in the world and the club is getting there.
"When you look at the club three years ago and where it is now, it is a big change. You never know where the club will be in three years.
"We just have to keep working really hard, keep believing in what we are doing and I am sure the club will challenge the biggest in the world."
Vieira will primarily be remembered as an Arsenal legend after making 372 appearances and winning three league titles during nine years with the Gunners.
He only made 12 league starts after joining City in January 2010, but the club made a huge impression on him and he was keen to stay in some capacity after deciding to retire.
Vieira, who also won 107 caps for France, said: "It was time for me to hang up the boots but I am really happy with my new role.
"I have been at the club for a year-and-a-half but I feel like I have been here for 10 years.
"The football club is growing up so fast and I am really proud to be part of it.
"It is a hard decision but it was easy at the same time because the proposal from the club to work for them was exciting.
"I wanted to learn the other side of the game as well, and what a club to do it at."
Vieira was speaking as City unveiled ambitious plans for a new 80-acre, state-of-the-art training complex near to the Etihad Stadium.
As part of the recently-announced Etihad Campus project, the club intend to develop a world-class facility for their first team and academy.
"It is fantastic, unbelievable," said Vieira. "When you are a player what you ask for is a facility where you can express yourself and learn.
"I don't think you will find a better facility than this around the world."
Source: Team Talk
Source: Team Talk