According to Pro Sport, Cluj are pursuing the 32-year-old winger, who is currently a free agent after his stint with Qatar's Al Duhail, wrote Moroccoworldnews.com.
The push for Ziyech comes courtesy of recruitment advisor Mikaël Silvestre, who previously played a key role in bringing Islam Slimani and Marcus Coco to Cluj, alongside club president Ioan Varga.
Ziyech has reportedly requested a few days to make a decision together with his family, amid interest from Ajax Amsterdam.
CFR Cluj are hopeful of convincing the former Chelsea star to join their ambitious project as they continue to bolster their squad with experienced international talent.
Valued at around 4.5 million euros, Ziyech enjoyed an illustrious European career, shining at both Ajax and Chelsea before moving to Qatar.
His potential arrival would mark another significant coup for Cluj as the club aims to assemble a team capable of competing at the highest level.