The Gunners missed the chance to briefly go top of the table on Saturday as they were held to a 1-1 draw at Sunderland.
Now Arsenal find themselves four points adrift of Chelsea, with the rivals due to meet at Stamford Bridge on Sunday October 3.
Denilson, however, insists the Gunners are capable of winning the title.
He said: "I still think we can win the Premier league this season.
"For me Arsenal are the best team. If you look at Barcelona we play like them and I can see Arsenal winning something this season. We have the players and we have the touch. Chelsea have very strong players but they are older. And I think that Arsenal are going to win a trophy. This was just one game and we are still in a good position."
Darren Bent's equaliser deep into injury-time at the Stadium of Light denied the ten-man Gunners all three points but Denilson insists a draw on Wearside is no disgrace.
He said: "You can not expect to win at Sunderland because they have beaten the best sides over the years here and it was always going to be a big game. It doesn't matter who you play against - whether it is Chelsea or Sunderland - it is always difficult away from home."
"It is not right to say we are not ready to win the league just because of this result. It was tough when it went down to 11 v ten but we showed our quality. We were playing very well and we looked as though we would hold on."
Denilson understands the frustrations of the fans, who have high hopes that their young side will deliver some silverware this season after five barren years, but the Brazilian still believes the Gunners will be celebrating at the end of the season.
He said: "It has been a long time since we have won the league and I believe this season we will win some trophies. I am confident because we have shown all the time in games how well we can play and the spirit is there as well.
"I joined in 2006 and I can understand the fans being impatient but we have the best manager here who tries not to put us under too much pressure. We all have to show him how much we want it.
"In training we work together and we have definitely got a chance of winning something. We have some very good young players coming through such as Jack Wilshere."