The Frenchman ended his stellar playing career with City at the end of last season and has now become an official club ambassador.
And, while he notes many experts are predicting the champions will once again be from the other side of Manchester, at Old Trafford, Vieira has faith in his own club.
"We can win the title," he said.
"We have improved since last year. Winning the FA Cup and finishing third has given us the belief.
"We believe we can challenge Chelsea, Manchester United and the rest of the teams to lift the championship."
Much may depend on what happens over the next few days.
Samir Nasri is edging closer to becoming the latest player to leave Arsenal for the newly-named Etihad Stadium.
However, that deal, likely to cost the Blues around ?24million, comes with no guarantees in itself and Nasri will need to produce his form of the first half of last season rather than the second, with French national boss Laurent Blanc noting a reduction in the midfielder's standards this week when Les Bleus could only draw with Chile in Montpellier.
Record ?38million forward Sergio Aguero is still to kick a ball in a match for his new club and the future of his fellow Argentina star Carlos Tevez remains unresolved, as does the issue of who will be skipper for Monday's opener against newly-promoted Swansea.
The chances are controversial Italian Mario Balotelli will be involved after yet another turbulent week in the 20-year-old's fledgling career.
So poor was he in last weekend's Community Shield, Gary Neville felt compelled to describe Balotelli as "an embarrassment".
Yet Vieira, who worked alongside the former Inter Milan player in both Italy and England, is prepared to give Balotelli time to mature.
"People forget how young Mario really is," said the former Arsenal skipper.
"He is a really young boy. He will make mistakes. I made a few in my career.
"Hopefully this year he will learn from them.
"Mario is a really talented footballer and I hope he can show everybody how good he is."
Source: Team Talk
Source: Team Talk