The former Gunners midfielder insists the club are not dead and buried yet, but admits they have to improve their faltering home form.
The Gunners stayed within 11 points of leaders Leicester City with a game in hand by returning to form to cruise to a 2-0 victory over Everton at Goodison Park at the weekend.
However, Arsene Wenger's side have won just two of their last eight matches in all competitions at the Emirates Stadium, a run which includes defeats to Watford and Swansea City and failure to break down Southampton and Hull City.
Five of the North London side's remaining eight fixtures are at home, with every one of those against a team currently in the bottom half of the table, and Parlour insists that a 100% record from those fixtures would resurrect the club's title ambitions.
The 43-year-old told Sky Sports: "I think they've got to still be alive. They've got five home games left, but three tough away games - West Ham, Manchester City in the second from last game of the season and Sunderland, who will be fighting for their lives.
"But their homes games you would expect them to win. That's going to be the problem, their home form - is it good enough? We saw them get beaten by Swansea and Watford in the FA Cup, so they've got to improve on that.
"Away from home, it hasn't been too bad - a good performance against Everton, who were pretty poor, but Arsenal had to do what they had to do. [Wenger] will be saying to be positive and to keep going. Arsenal have just got to stay in there and hope that Leicester and Tottenham make a mistake."
A major thorn in the side of Arsenal's ambitions in recent years has been their tendency to struggle to break down certain lower-table clubs in front of their own fans, and that weakness has reared its head again in recent weeks.
After a run of just three wins in their last 10 Premier League matches since 2 January, the Gunners have the bare minimum of margin of error in their remaining eight games.
Even if they win their game in hand, they must make up an eight point deficit across the other seven matches if they are to clinch a first league title since their 'Invincibles' success of 2003-04.