The midfielder has spent the season loaned from the Gunners at his former club, which he left for £3.4 million back in 2006 to move to London.
Having fallen out of favour at the Emirates, Denilson returned to Sao Paulo in the summer. With the club currently joint-top of the Campeonato Paulista, club vice-president Joao Paulo de Jesus believes the 24-year-old now wants to stay.
De Jesus said: "Our conversation was that we have every interest in continuing as we are. We want to renew at the end of the contract and he has said he wants to too.
"He will speak with his representatives, who will contact the English club. There is no rush because he is here until the middle of the year."