City are prepared to offer Van Persie big money to swap the captain's armband at Arsenal for the prospect of a Barclays Premier League title.
Vieira told the Daily Mail: "Robin van Persie will make the best decision on his future. He is 29, with a year left on his contract, and can make his choice.
"It is difficult to believe that Arsenal are such a big football club and they haven't won anything since 2005 - now there is pressure. They need to win something to have respect worldwide.
"Podolski will be an important signing because he has the mentality Arsenal need. They have been lacking leadership on the field."