Arsene Wenger’s side go into Wednesday’s crucial meeting with fellow Champions League aspirants Liverpool four points adrift of fourth-placed Spurs.
Despite the Spanish side’s insistence that the former Valencia man is not for sale, the Gunners continue to be heavily linked with a deadline day move for the 31-year-old.
Parlour, however, a vital member of Wenger’s last title-winning side in 2004, believes that the recent form of summer recruit Olivier Giroud, who has scored four goals in his last two games, means that a failure to secure Villa’s services would not represent a terminal blow to his old side’s ambitions.
“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," he told talkSPORT “I’m sure the scouting system is working hard to find players for Arsene Wenger, but nothing has fit the bill."
He added, “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."