The Frenchman moved to Stamford Bridge in January and after a slow start, found his form and went on to play a key role in his country lifting the World Cup in Russia.
A late return from the tournament has meant he has had to remain patient behind Alvaro Morata but despite still being to score a goal for the club this season, seems to have moved ahead of the Spaniard in the pecking order.
Despite seemingly being first choice, Giroud's contract is set to expire in 2019 and he has been regularly linked with a move back to France.
Marseille have tried to sign him in each of the last two summers and are thought to be monitoring his situation.
The former Montpellier man seems happy with the Blues though, insisting he'd be foolish to leave a club with so much success in their recent past.
He told Maxifoot: 'OM's interest this summer? It did not go as far as has been mentioned.
'There was contact last year, but nothing really concrete this summer. I had just arrived in Chelsea and I did not want to pack my bags again three months later.
'For me, Chelsea is the top club in England, the one that has won the most titles in the last 10 years. So, why leave?'