That's according to Gunners legend Martin Keown.
The North London team endured a tough final campaign under Arsene Wenger last season, finishing sixth in the Premier League and not qualifying for the Champions League.
Emery took over after his departure from PSG and the Spanish has the task of guiding the Gunners back to the race for the title.
Arsenal has strengthened well this summer, bringing five new faces, including Uruguay World Cup star Lucas Torreira.
"I would not have thought that Arsenal could win the league."
Legend of Arsenal Martin Keown
This afternoon, they have their new campaign underway and Emery faces a difficult first test when he hosts Manchester City in the Emirates.
Keown is aware that this season will be highly competitive and there are several contenders competing for a place in the top four.
But the former defender insists that his former team is more than capable of recovering from last year's failures.
"It's difficult," he said exclusively to Starsport.
"Because the previous manager used to say that the first four were something to be proud of and now I think the club would really settle for being among the top four again.
"Because there is a transition period, a new manager will come in after the age of 22. You have seen the impact of Sir Alex Ferguson's departure.
"I know (United) they were winning trophies and Premier Leagues, Arsenal, well, they have not won one since 2004.
"So I think Arsenal could really challenge the first four positions, I would not have thought that Arsenal could win the league.
"They will consider him optimistic, but I am sure he is beyond them when you look at the quality of City and Liverpool, of what they are forming.
"And then it's a case where you look at Chelsea also outside the top four." Arsenal, Chelsea, Manchester United maybe all go for the fourth place.
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"Tottenham will have a hard time dealing with the fact that a large part of his team has not yet returned.
"They have to move after Wembley, they just have to play a game at Wembley and then they'll go back to their natural home again.
"I'm sure the impetus of that, the pull of that will see you start reasonably well.
"So it's going to be difficult for Arsenal to enter the top four, but I think it's something they're capable of."
Martin Keown was speaking at the FA Football and McDonald's AF Awards of 2018, celebrating grassroots heroes across England.
Discover more: www.mcdonalds.co.uk/grassroots