The 32-year-old has been with the Canaries since 2009 and has helped them on their rise from League One to the Premier League.
However, he has been linked with a move away from Carrow Road in recent weeks and following a flurry of bets, Sky Bet have stopped taking money on the centre-forward's next club being Championship side Wigan.
"We had to pull the plug on Holt's market due to the sheer volume of bets we've taken on," said the company's football trader Chris Spicer.
"Our customers have been queuing up to back the move, which was an even-money price just two days ago and as long as 8/1 last week."
Holt scored eight goals in all competitions last season.