The 27-year-old joined Arsenal from Montpellier in 2012 and has already scored 15 goals in his 40 appearances for the Premier League side.
Giroud has made a strong start to the season, leading Arsene Wenger's attack with four goals in the opening six matches in the English top flight.
However, despite harbouring big ambitions, Giroud is determined to stay grounded in order to make sure he can achieve all his goals.
"What has always made me succeed is the fact I set sensible objectives," he told France Football. "I grew that way, step by step. Before thinking about Ballon d'Or, before being part of the top 10 players in the world, I first have to be in top 10 forwards in England.
"I am starting to make a name for myself among that top 10 and I want to do it this year. That is a short-term objective.
"Talking about that two years ago, I would have said it was not sensible. Now I am aware I have the right potential to make it."
The Arsenal faithful at the Emirates have soon warmed to Giroud and the attacker is relishing the warm welcome as he starts to settle into the club.
"Fans chanting my name is really great," he added. "I am very proud of that. It is great honour to have been adopted by the fans so quickly. That gives you desire to pay back on the pitch. I think they feel I give my very best. I don't only think about scoring.
"The second seasons are always difficult. Last season I scored and assisted so people will ask for more. So, more expectation and more pressure.
"When I joined the club of course I put myself under big pressure may be too much because I replaced Van Persie. Frankly early last season, I didn't make the right gestures, I was tense. I was stiff like a stick."
Giroud received his first international call-up from Laurent Blanc in 2011 and is now locked in a battle with Real Madrid's Karim Benzema to lead the French attack.
Despite admitting the pair are good friends, Giroud believes he currently holds the advantage.
"We have a very good relationship, but indeed we are in competition," Giroud conceded. "Of course I am a candidate for the centre forward position in the French team. Of course I want to play but you can't ask for it, you have to deserve it.
"Against Georgia I think it was nice the coach substituted Karim and not me. And the fact he played me in Belarussia, even if I have a lot of respect for Karim, it was legitimate he put him on the bench. The coach was fair."