The former Arsenal man has advice for Arsene Wenger.
The Gunners enjoyed an excellent start to the transfer window by signing midfielder Granit Xhaka for £34 million, but it has been an underwhelming six weeks or so.
Arsene Wenger has since signed unknown Japanese striker Takumo Asano and 20-year-old defender Rob Holding - neither of which are likely to be prominent figures in a Premier League title-winning team this season.
Arsenal finished 10 points behind champions Leicester City last term in a season which saw a number of the big boys fail to turn up - but the same most probably will not happen again.
Chelsea, Manchester City and Manchester United, under Antonio Conte, Pep Guardiola and Jose Mourinho, will surely come back much stronger this time around and Arsenal have only signed one established player.
It seems unlikely that Xhaka on his own will be the difference between success and failure this season, and Parlour, who won three Premier League titles under Wenger at Arsenal, feels that his former boss needs at least two tried-and-tested reinforcements.
"They need a centre-half, for me, and they need a centre-forward," he told talkSPORT. "I think the midfield they're very strong, but a centre-half for me is key, to play alongside Koscielny.
"And they need a guy who's going to score you goals. Giroud is a good player, no dobut, but he does probably need four chances to score one."
Olivier Giroud is their only established striker. Plenty have been linked, including Gonzalo Higuain, Mauro Icardi and Alexandre Lacazette.
But it remains to be seen whether Wenger coughs up the significant sums needed to prise one of these boys away from their clubs.