The Dutchman's stint in South Yorkshire has been hampered by injury problems and form issues since has arrival at the club in August 2017 when he joined from Eredivisie outfit Heerenveen for around £3m.
Van Aken's last appearance for the Owls arrived in the Carabao Cup tie at Sunderland almost a year ago.
His last outing in the league came in the 3-2 loss at Wigan on the opening day of last season.
The 25-year-old was linked with moves to NAC Breda, FC Emmen and PEC Zwolle last summer with the defender keen to end his fraught spell in England and head back to the continent.
Van Aken will remain contracted at Osnabruck until the end of June 2020.
The defender's Owls deal runs out in the summer of 2021.