Giroud won back his place in the starting line-up in Saturday's 2-1 win over Everton and the France international seems to have found his goalscoring touch after an inconsistent start to the season.
He scored six goals in his last seven appearances for club and country.
"I don't want to look too far forward because we need to keep it up and carry on this momentum. It's only the 10th game in the league so we've got 28 to go, so it's a bit early," Giroud told the club's website (www.arsenal.com).
The 29-year-old said Arsenal's fighting mentality will be crucial if they are to lift the league trophy for the first time since 2004.
"I think we are stronger mentally this year," Giroud said.
"We are all fighting for each other. We have a great togetherness and we want to achieve big things altogether. We are showing a lot of leadership."
"We are all looking in the same direction and we know we need to be 100 per cent in every game. If someone is a bit tired then someone else will battle and fight for each other. That's the mentality we need to show through the season."
Injured midfielder Jack Wilshere feels Arsenal need not sign any players in the January transfer window as the squad is strong enough to compete for top honours.
"I don't think so," the 23-year-old said when asked if the club need to strengthen the squad in January.
"Defensively we look good. We've got Gabriel who has really grown up. Last season, he was settling in. He is really suited to the Premier League.
"We've also got myself and Danny Welbeck who should be back round January and make the team stronger."
Arsenal will hope to keep the pressure on Manchester City at the top when they travel to Swansea City on Saturday.
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Sudipto Ganguly)
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