The winger, who scored 19 times in the Eredivisie, can play on the right-wing or straight through the middle.
Norwich want Berghuis to help fill the void left by the departure of Emi Buendia.
The latter secured a move to Aston Villa earlier this transfer window.
The Press Association claims that 28-year-old Berghuis could leave De Kuip for a modest fee this summer.
A transfer could happen for between four and five million euros.
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!