The Gunners have so far signed Alexis Sanchez, Calum Chambers, Mathieu Debuchy and David Ospina, with the outlay coming to around £60 million.
It is the arrival of £32 million striker Sanchez that has really whetted fans' appetite this term, and the Chile international went some way to paying back his hefty price tag with the winning goal against Besiktas on Wednesday evening.
The former Barcelona star netted on the stroke of half time as the Gunners squeezed past the Turkish side at the Emirates, but Olivier Giroud's injury has given Arsene Wenger a worry over a lack of options up top.
Yaya Sanogo is still relatively untried in the Premier League, while Nicklas Bendtner, who deputised for Giroud occasionally at times last season, left the club in the close season.
Giroud is expected to be out until the New Year with a broken foot, and Hasselbaink, who played at Stamford Bridge from 2000-2004, thinks Wenger will have to add another centre-forward to his ranks.
The Dutchman also explained that the North London side need a dominant central midfielder before the September 1 deadline.
He told Sky Sports News: “Especially since Giroud has got injured, I definitely think that Arsenal need a striker, a goalscoring striker.
"I think Wenger is a very smart man doesn’t give a lot away, but he’ll be looking into the market as to what is available at this moment.
"For me they need a sitting-midfielder, someone with legs and someone who is mobile, [They] need someone can get around the pitch. I also think they are lacking there as well."
The Gunners have points this season having followed up their 2-1 win over Crystal Palace last week with a 2-2 draw away to Everton and they play Leicester City this Sunday at the King Power Stadium.