The Gunners have failed to add any new players to their squad so far this month, and currently lie sixth in the table, four points adrift of rivals Tottenham Hotspur in fourth.
"I really thought he might go and strengthen, at least bring in one player in, but it appears David Villa didn't want to come to Arsenal," Parlour told talkSPORT.
"I'm sure the scouting system is working hard to find players for Arsene Wenger, but nothing has fit the bill.
"It looks like he's not going to buy anyone at the moment and he'll have to go until the end of the season with the squad he's got. If Olivier Giroud can bang a few goals in then he can fire them into fourth place."
The Gunners drew 2-2 with Liverpool at the Emirates Stadium on Wednesday.