The 20-year-old South Korean striker has allegedly attracted the interest of the newly promoted German club who recently signed compatriot Cha Du-Ri
Voetbal International claims Fortuna have already contacted the agent of the 20-year-old, who is currently on the books of Eredivisie club Groningen.
However, according to the report, Fortuna are yet to contact Groningen about the player who has a contract with the Dutch club until 2013, with an option for a further two years.
Groningen may be interested in selling the Chungju-born forward following the recent signing of Netherlands Under-21 striker Genero Zeefuik, however no deal will be done until after the 2012 Peace Cup where the Dutch side will compete, with Suk's participation part of the agreement.
The 2012 Peace Cup, to be hosted in Suwon, will run from July 19 to 22, including Groningen, Hamburg, Sunderland and Korean club Seongnam Ilhwa.
Suk scored five goals in 20 appearances for Groningen during the 2011-12 season after moving to the club from Ajax Amsterdam.
Dusseldorf recently signed another South Korean, full-back Cha Du-Ri from Celtic.