The Gunners won the FA Cup last season but finished fourth on the Premier League table and were knocked out at the Round of 16 stage of the Champions League.
Despite winning their first piece of silverware since 2005, Arsenal were off the pace in the league race and French defender Koscielny feels they need to strengthen in each position to challenge the likes of Manchester City, Chelsea, Manchester United and Liverpool.
"We'll need a goalkeeper, a right back, a midfielder and a striker," Koscielny said.
"Winning the FA Cup can change things and lead to other players coming."
He added: "Yes, we need to recruit a very, very good striker, because it's important for us, for competition for places, because Olivier needs that to become even better.
"Having a striker who scores more than 30 goals a season can help us win the Premier League. Compared to the squads like Manchester City, even United, Chelsea. ... You can see there's a certain difference."
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