It is reported that De Zeeuw will be training with Sheffield Wednesday in the coming days to prove himself to his prospective new employer.
Wednesday this week announced Carlos Carvalhal as new head coach.
De Zeeuw is a free agent after his contract with Dutch side NAC Breda ran out at the end of last month.
The central midfielder is 32 years old, and has 27 international caps to his name for Holland.
The last of his caps came at World Cup 2010, when he played 45 minutes in the semi-final against Uruguay.
De Zeeuw has experience playing for Go Ahead Eagles, Anderlecht, and Spartak Moscow - and won Eredivisie titles with Ajax and AZ Alkmaar.
Wednesday are scouring the market looking for potential new signings with owner Dejphon Chansiri pushing for his side to challenge for promotion next season.