Giroud was linked with a number of clubs after a lack of starts in the Premier League last season, but the Frenchman eventually decided to remain at the Emirates Stadium and scored his 100th goal for the club against BATE Borisov on Thursday night.
However, Koeman has claimed that he targeted the striker as a replacement for Romelu Lukaku, who left for Manchester United ahead of the start of the new campaign.
The 54-year-old is quoted by The Express as saying: "When we sold Lukaku, I didn't think at that time we would get a striker in who would score at least 25 goals because maybe it is impossible to find that striker. What I expected was to get more goals from other players around the striker.
"That was the reason we needed a target man because that gives options for the team and finally we did not find a good target. We thought we had Olivier Giroud and that didn't happen."
A failure to sign a new forward during the closing stages of the transfer window has led to Koeman handing a chance to Oumar Niasse, who had initially been frozen out of his plans.