Per the source, Advocaat has instructed Fenerbahce scouts to keep tabs on Van Dijk and has made the Dutch defender an end of season target.
Advocaat knows Van Dijk from the Netherlands national team setup and has close ties to the 25-year-old defender.
The experienced manager has managed to get the best out of his Dutch players this season with on-loan Sunderland winger Jeremain Lens and Robin van Persie excelling for the Yellow Canaries.
Advocaat replaced Vitor Pereira with just a week before the end of the transfer window and was unable to mark his stamp on the current squad as a result. The head coach plans to make changes to the squad over the winter and summer transfer windows to build a side that he feels can compete in the Champions League.
The report claims that Van Dijk will set United back £30 million to prise the powerful defender away from the Saints.