It was a bold claim, and has proved a little unfounded. Podolski has spent the majority of his time on the left-wing, while Giroud has impressed in spells but shown himself to be a very different kind of centre-forward.
While more able in the air than the Dutchman, he lacks Van Persie's finishing prowess. Giroud sometimes needs a couple of chances to score a goal; Van Persie rarely needs more than a half-chance.
The idea was to spread the goals out around the team. Wenger hoped that Giroud, Podolski, Theo Walcott, Gervinho and others could share the burden. It was an idealistic but ultimately unrealistic vision. The reality is that trophy-winning sides usually contain a striker who scores 20 to 30 goals.
For Arsenal to step forwards rather than back, they needed to use Podolski and Giroud to supplement a striker in Van Persie's mould.
Instead, they have been left with relatively meagre attacking options. When Giroud has been absent, Arsenal have been forced to turn to Gervinho, who is at best an enigmatic winger, and Marouane Chamakh, who is surely on borrowed time with the club.
Giroud needs support, and Arsenal need a poacher: someone who can be relied upon to score the crucial goals in those tight games. This season alone, Arsenal have drawn blanks against Sunderland, Stoke, Norwich, Villa, and Swansea. If they are to pick up the points required to secure Champions League qualification, a striker is a necessity.
The two men in the frame are Demba Ba, linked with Arsenal by The Sun, and Fernando Llorente—a potential deal mentioned most recently in The Daily Telegraph. Both have differing kinds of pedigree. Ba has proven himself in the Premier League with both West Ham and Newcastle, while Llorente's experience has come in La Liga with Athletic Bilbao.
Llorente, meanwhile, is six months from being able to leave Bilbao on a free. He has been frozen out of the first-team picture there, and Bilbao may choose to let him go for a reduced price in January rather than let him sit out the remainder of his contract.
So which player would suit Arsenal better? Of the two, Ba is the more mobile. He is rangier and makes more runs in behind the defence. Llorente arguably has a better touch and superior heading ability, but doesn't provide the same range of movement. In fact, Llorente is not hugely dissimilar to Arsenal's existing first-choice striker, Giroud.
Who should Arsenal sign?
It is for that reason, were I holding the purse strings at Arsenal this winter, I would go for Demba Ba. He offers greater variety, and with Premier League experience behind him, could hit the ground running.
Signing a player from abroad always brings with it a degree of risk—while Llorente seems impressively physical in La Liga, could he cope with the rough and tumble of the Premier League? At best he would require a period of adaptation, and in the race for the Champions League places that is time Arsenal simply don't have.
The one caveat with Ba is his history of knee problems. There are concerns over whether or not his injuries could flare up in future. Arsenal ought to be heartened by the fact that other players like Mikel Arteta have had considerably improved injury records since joining the club. I would say this: considering Arsenal's need and Ba's quality, at £7.5m he's more than worth the gamble.