The Canaries are keen to bolster their squad ahead of their return to the Premier League and have already signed the likes of Milot Rashica, Pierre Lees Melou and Billy Gilmour.
Daniel Farke has strengthened his attack with the signing of Rashica from Werder Bremen, but wants to add at least one more player to his strike force.
PAOK winger Tzolis has emerged as a target for Norwich, who have opened negotiations with the Greek top flight club over a deal for the 19-year-old.
The Premier League side made an initial offer of €9m in an attempt to acquire Tzolis’ services from PAOK, but saw the bid quickly knocked back down by the player’s employers.
Despite seeing their initial offer for Tzolis turned down, Norwich are expected to go in with a second bid for the teenager.
While Norwich are tipped to make a second offer, it remains to be seen how much the Carrow Road outfit are willing to pay for the Greece international.
Tzolis has attracted interest from some of Europe’s top clubs, with Manchester United and Borussia Dortmund said to have scouted the 19-year-old.