Giroud has a Ligue 1 title to his name, as well as the FA Cup and a World Cup with France this summer, but admits he is jealous of his Chelsea team-mates who have already triumphed in England.
"I prefer to be at a big club rather than playing every week in a less prestigious team and I still have targets," Giroud told the 'Guardian'.
"To win a Premier League is my last dream as a footballer, maybe more than winning a Champions League, because I know how tough it is to win this league.
"I have team-mates here who have won it, so I'm a bit jealous. I want to make it happen.
"Look, I know we we lost at Wolves but we beat Manchester City, so don't count on me to give up on that dream just yet. I don't want to end with any regrets."