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.