The former midfielder has also suggested that a move for Real Madrid's Karim Benzema was never going to happen.
The French boss was looking comfortable with the Gunners last term, after they won their second successive FA Cup following an impressive run of form in the second half of the campaign.
That had many touting them as Premier League title favourites, however, a poor transfer window in which they only brought in Petr Cech has left many questioning what is going on at the Emirates.
And Parlour has suggested that failure to improve could see Wenger fall under the microscope if results do not go as he would like.
“It’ll be interesting to see what happens now because he’ll be under pressure Arsene Wenger,” he told Fletch and Sav.
“If they start losing a few games, they’ll be looking back. It [the transfer window] started really well with Cech; I thought that was a great signing. Everyone was waiting for a big outfield player, they had Ozil two seasons ago, Sanchez last summer and it just didn’t happen.”
Karim Benzema move was never going to happen
The former Arsenal midfielder has also suggested that a move for Karim Benzema was never going to happen.
The Gunners were linked with the Real Madrid striker in a big-money move all summer, with many believing that he would be the ideal signing to improve their forward line and push them closer to a title challenge.
It never came off, though, with a deal never looking likely despite the numerous rumours, and Parlour believes he was never going to be allowed to leave Spain.
“The fans are saying now, where’s the money going, we want to spend that money,” he added.
“Benzema was mentioned but I don’t think he was ever available; Real Madrid had to keep him. With Bale and Ronaldo up front they’re going for the Champions League and La Liga. It’s going to be interesting to see what happens.”