The Italian was named sporting director at Wolves over the summer.
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Teti had worked with Pereira at Al Shabab and with the latter's dismissal, he has now followed the former manager out of Molineux.
Wolves chairman Jeff Shi stated: “Domenico has fulfilled his role with great professionalism, building solid relationships within the club.
"He has made a positive contribution to our processes and has always conducted himself with integrity. We thank him and wish him all the best for the future.”