The north London side have been widely criticised for their failure to mount a serious Premier League title challenge in recent seasons.
Indeed, Arsenal have not won the Premier League title since their famous unbeaten triumph back in the 2003-04 campaign, when Vieira was still playing for the Gunners.
The north London side were held to a thrilling 3-3 draw by Liverpool FC at The Emirates on Friday night as they failed to take their opportunity to move into the top four.
Arsenal are bound to be linked with a host of players in the coming days and weeks as the January transfer window draws ever nearer and Wenger considers bolstering his squad.
And Vieira believes that the north London side should do what they can to bring in significant reinforcements in the January window.
Speaking to Sky Sports on Friday night, Vieira said: “When you look at the Arsenal team in the last few years I think everybody will expect more from Arsenal because of what this football club represents.
“In the current years of course it’s not good enough.
“It’s not good enough for the club, it’s not good enough for the fans.
“Of course when you are used to winning, you want to keep winning.
“There are players who have to make a decision about what they want to do in the future and that is the first thing they need to resolve.
“Then bring in quality players to challenge Manchester City because I believe that Manchester City will be the team to beat in the years coming.”
Arsenal return to Premier League action on Thursday night when the take on Crystal Palace at Selhurst Park.
The north London side finished fifth and missed out on Champions League qualification last season.
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