The Denmark international is a free agent after leaving AZ on a Bosman free transfer, and is now expected to continue his career in Spain with the newly-promoted side
The newly-promoted Primera Division outfit were in the market for a new left-sided player due to the departure of Andres Guardado to Valencia, and see the 27-year-old as the ideal replacement.
Poulsen joined AZ from Midtjylland in January 2008, and eventually developed into a key player at the Alkmaar side after being converted into a wing-back from a left winger.
The Denmark international turned down an offer from AZ to extend his stay at the Eredivisie side, and has since been linked with Ajax, Aston Villa and Borussia Monchengladbach.
Nevertheless, he has now opted to join Depor instead, and is expected to sign a two-year deal in the upcoming days.