It has been six years since they were last crowned domestic champions but Denilson insists Arsene Wenger's side are ready to realise their potential.
Arsenal trail United by two points with seven games remaining and have the easiest run-in of the title rivals, while Wenger has claimed they are capable of upsetting Barcelona in the Champions League.
"What's coming up is a great opportunity for all of us," Denilson told the club's matchday programme.
"I think we have gained from the experience of last season. We were in good positions in some of the competitions but missed a little bit.
"At the start of the season, though, I was telling people I thought we were ready because we were close and focused.
"And you can see now that we are strong and well placed.
"We have a good opportunity to win the Premier League and are in the last eight of the Champions League.
"The boss has just told us to focus and as players we know we need to win something."
Denilson has developed a reputation as a long-range specialist after striking six goals in 23 appearances this season, most of them from outside the area.
"It seems to have become my speciality to shoot from long distance," said the Brazilian midfielder.
"Sometimes when I shoot I put a little swerve on the ball which can make things difficult for a goalkeeper.
"Our team always passes the ball or crosses, ultimately shooting in the box, but people sometimes say you never see the Arsenal team shoot from distance so I try.
"I do this a lot in training, staying after our team sessions sometimes to practice with one of the goalkeepers and if I have the opportunity, I will give it a go."
Denilson hopes to play a full role in the remainder of Arsenal's season.
"It has been different from last year, when I played most games," he said.
"This time I've been injured a bit and on the bench a few times too.
"But I just say that I am feeling good now and ready for the rest of the season."
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