The Gunners have fallen away in the title race this season.
The Gunners have once again failed to challenge for the Premier League this season, having fallen away in 2016.
They did lead the table at the start of the year, before a dreadful run of form has left them 13 points behind leaders Leicester City with just five games remaining.
That has led to criticism from the fans, who believe this year should have seen their side challenge given that rivals such as Chelsea and Manchester City have struggled.
Instead they must now wait until next season at the earliest, with many feeling they need several new faces to arrive in the summer for a chance next season, and Parlour concurs.
"They will be disappointed, they had a really good chance of winning the league. They have come up short again," Parlour told Sky Sports News HQ.
"He needs to make some big signings, there is no doubt about that. In the summer transfer window they need to go out and get these players to put them on to the next level like City and clubs like that.
"He'll [Wenger] look around the dressing room and say to himself, 'have I got enough here to win the title?' And hopefully, if he can buy two or three next year, he might have a chance."
Of the areas that Wenger will surely look to improve, the striker position must surely be top of the list.
Olivier Giroud had impressed earlier in the campaign but has struggled in the second half of the season, while Theo Walcott has failed to impress when given his chance in a central role.
Who Arsenal could sign is debatable, although a recent report from the Telegraph says Juventus striker Alvaro Morata is top of the list.