With just eight games remaining, Arsene Wenger's side are 11 points adrift of leaders Leicester, albeit with a game in hand.
Arsenal were top of the table at the turn of the year, but a run of just one win in their last four league outings has left them third, behind both Leicester and local rivals Tottenham.
After their elimination from both the FA Cup and Champions League, Arsenal's season is in danger of petering out.
But Ozil, who played in Germany's 3-2 defeat to England on Saturday, said he felt Arsenal could still turn the situation around.
"I do not think it impossible," he told German newspaper Welt am Sonntag when asked about the possibility of Arsenal catching Leicester and winning the league.
"Although there are only a few games left, Leicester have a run against some of the big teams to come.
Didier Deschamps says Olivier Giroud's lack of goals for Arsenal has not affected his ability to score for France.
"We ourselves must in any case not allow any more slip-ups. The hope of the title is still there -- we have the players for the title."
A 2-0 win at Everton before the international break kept Arsenal's hopes alive as they look for a first championship in 12 years.
They face Watford, the side who knocked them out of the FA Cup at the quarterfinal stage, next weekend and Ozil knows focus is key.
"We see in every game that players of Leicester want to achieve something. We ourselves have not been focused in every game, and that is not possible in the Premier League since there is no opponent you can beat easily," he said.
"Leicester have been great, but there are still a few games. I think we still have a chance to catch up Leicester. We must, of course, hope for mistakes."
Ozil said he expected Arsenal to bring in new players in the summer to maintain their challenge, especially with Pep Guardiola moving from Bayern Munich to Manchester City.
"We know that it will not be easy and that we need reinforcements if we want next season to be on top here again," he added.
"It is again interesting to see who invests in who and how much the clubs do during the summer break.
"In addition, great coaches are coming into the league. I am thinking primarily of Pep Guardiola. Wherever he has been, he had success. He is a coach, keen on playing and his teams are feared.
"He will be imprinting his football in England, and people will be surprised."