The 20-year-old has made a big impression at the Amsterdam Arena since making his debut in October 2012 and the club are keen to extend and improve his current deal, which runs out in 2015.
Overmars is understood to have met with the player's agent Winny Haatrecht on Monday to thrash out a new agreement.
"We are very satisfied with the development of Stefano and want to reward him for that," he told De Telegraaf.
Denswil - who has represented the Netherlands in every youth age group since under-15s - has made 11 Eredivisie appearances for Ajax this season and scored one goal in five UEFA Champions League matches.
Ajax are also looking to secure the future of 18-year-old attacker Ricardo Kishna, with the player confirming: "The club and my agent, Mino Raiola, are talking about."
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