In January, the Barclays Premier League club made at least three failed bids – around £6million being the highest – to lure the Hoops ace to Carrow Road.
Celtic held firm, but with the 24-year-old's contract at Parkhead now entering its final year, Chris Hughton's side were reportedly ready to come in with a lower offer in this window.
That plan looks to have been abandoned with Norwich bidding £4.7m for PSV Eindhoven's hitman Nils Ola Toivonen.
Having already agreed to purchase Ricky Van Wolfswinkel from Sporting Lisbon for £8.5m, they have decided to invest their remaining budget for strikers on the 26-year-old Sweden international.
Neil Lennon accepts he faces an anxious summer as he tries to hold on to Hooper. But the news one of the clubs leading the race for him is on the verge of signing another striker will offer some relief.
Talks with the man the Celtic manager would like to pair with Hooper up front, Amido Balde, are expected to continue into a third day.