Chelsea are the early pace setters after seven games, having gone unbeaten in all their league fixtures so far.
Manchester City, who Vieira is now a coach with, are in second place, five points behind the Blues.
But the Gunners, Vieira's former side, and Liverpool, last season's runners up, are in eighth and ninth respectively after poor starts to the league campaign.
The 38-year-old, however, is refusing to rule them out of the running just yet.
“I’m sure we’ll challenge in all of the competitions. If you look at the first few games, you’d say the title is between City and Chelsea," Vieira is quoted as saying by the Daily Mirror.
“But people with more experience will believe Arsenal can still be there, Liverpool also, despite a bad start, because of what they did last season.
“I think what will make it really exciting is that I believe five or six clubs will be up there, challenging at the top."
Manchester City face a tough weekend as they host Mauricio Pochettino's Tottenham Hotspur side, although they beat them 11-1 on aggregate last term.
Chelsea, meanwhile, travel to Crystal Palace, with Arsenal hosting Hull City and Liverpool facing Queens Park Rangers.