The Gunners have not finished in the top two of the Premier League in almost a decade, but finally seem to be catching up with rivals Chelsea, Manchester City and Manchester United.
The North London outfit are second in the Premier League this season and are on nine-game unbeaten run, winning eight of those.
Giroud is confident they will be genuine title contenders next term if they can emulate their current form, avoid their annual injury crisis, and add a couple of useful players to the squad.
“Yes, I think we can,” the France international said. “Hopefully we will have less injuries and if we keep this group, with maybe one or two new players coming in, we can have a great season.
“I know we can still improve as we have been doing since I signed. I am proud about it and pleased with that.
“I just want to carry on like that and I know if we keep our best players, this determination and team spirit, I am sure we are going to join the championship race.”
Giroud has been in good form for Arsenal this season, bagging 18 goals despite spending three months on the sidelines with a broken leg.
The Frenchman reveals mental strength and believing in yourself, even when things aren’t going your way, are the keys to success.
“Mental strength is hugely important when you are a football player and even more as a striker. You have people who doubt your abilities and you have to believe that you can always come back,” he said.
“If you miss chances in one game, it is not because you have lost your talent or your belief. You have to be faithful to your qualities. That is part of being a player, being strong in your head.
“In football you have to question yourself every week, be ready in your head and you have to be 100 per cent determined if you want to keep going in the games.”