The Gunners claimed an impressive 3-2 win over Liverpool in the Premier League on Sunday at the Emirates Stadium.
They followed up last weekend's success over Tottenham with an even more impressive triumph, showing they are the real deal this season.
"The way we're going, we're doing well," White told beIN SPORTS after the match.
"Game by game - why not [win the league]?"
He added: "I think this squad is fantastic. I don't think there's anyone getting ahead of themselves. You can see that in the training we do during the week. It's game by game, we're not looking too far ahead."
He finished: "Playing against Liverpool is always tough. In recent years, we haven't gotten the results we wanted. This year is different. I don't think there's any fear in our team, we're all young and hungry to be the best, so that's what we're trying to do."