The Gunners ended last season 10 points adrift of champions Liverpool, following back-to-back runner-up finishes behind Manchester City.
In the Premier League era, Arsenal have finished second a record nine times, two more than Manchester United and no team has ever claimed that spot four consecutive times.
Now, Saliba is urging his teammates, including the new summer signings, to take the next step.
He told ESPN: “Of course we’ve finished second for three years in a row, and we know that we always miss something. Now it’s a new season, we have to see what we didn’t do well enough to win the league.
"We won the first game and of course we want to win the league, and we will give everything. We have to be better than the last three seasons to win this league.
"We know that the new players who came to help us, and I’m sure that they will help us to win some trophies. Of course we are already better with them. Let’s see."