Arsenal have 26 points after eight wins and two draws, having been held 2-2 at Sunderland last weekend, with Manchester City closing the gap following a 3-0 home win over Liverpool.
Mikel Arteta's team have conceded only five league goals so far, but Saka said they were not getting ahead of themselves.
"We just have to win every game, that's the mentality we go into the game (with) and see where it leaves us," he told talkSPORT in an interview published on Thursday.
"We cannot get carried away with what people are saying, because one day they say something and the next day they say something else.
"People's opinion about us changes like the weather. The most important thing is our dressing room, and the foundation and the belief we have in ourselves."
Arsenal have come second for three straight seasons under Arteta, falling short in 2022–23 and 2023–24 before finishing further behind last year, a sequence of misses that has left them still chasing their first league crown in two decades.
They next host fifth-placed arch-rivals Tottenham Hotspur on November 23rd following the international break.
Saka is preparing for World Cup qualifiers against Serbia and away to Albania on Sunday, with England having become the first European nation to seal a spot at next year's finals in North America with six consecutive wins in their group.