The France defender believes the FA Cup winners need more firepower, as well as replacements for Bacary Sagna and Lukasz Fabianski after they left the Emirates Stadium
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France striker Giroud scored 22 goals in all competitions for Arsene Wenger's side in the 2013-14 season, but supporters at the Emirates Stadium have been vocal in their belief that the club need further attacking options.
And Koscielny, who signed a new long-term deal at the club in May, believes a forward who can contribute 30 goals per season is required if the north London outfit are to challenge for honours moving forward.
"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," he told reporters.
"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 [Manchester] United or Chelsea, you can see there's a certain difference."
Chief executive Ivan Gazidis has revealed the club are already in deep conversations regarding potential targets, though it has been reported they aren't willing to match the €35 million bids of Chelsea and Manchester City for Cesc Fabregas.
Koscielny, though, is hopeful a midfielder will be added to the squad, as well as replacements for the departing Bacary Sagna and Lukasz Fabianski .
"We'll need a goalkeeper, a right back, a midfielder and a striker. It's important to have a minimum of these four players so that we'll be better able to challenge over the course of a whole season against teams like Manchester City, Chelsea or United.
"Winning the FA Cup can change things and lead to other players coming."