Voetbal International reported the news on Thursday evening. 41-year-old goalkeeper Remko Pasveer will reportedly also extend his contract and continue as the club's second-choice stopper.
Klaassen rejoined Ajax for a second time in 2024, signing a one-year contract in September after his contract at Serie A champions Inter had expired.
The midfielder had played 321 matches for the club in his two earlier periods between 2011 and 2017, and 2020 and 2023. After arriving as a free agent last summer, Klaassen played 35 games across all competitions, scored eight goals, gave two assists, and was nominated for the Player of the Year award by the Eredivisie.
His 356th game for Ajax, last Sunday's Eredivisie match against FC Twente, placed him in the top 10 for all-time games played, equaling the legendary Piet Schrijvers' total.