It is understood that the Canaries believe that a deal for the 20-year-old was becoming too expensive and have now opted to move onto other targets.
Sporting director Stuart Webber recently travelled to Canada to speak to Kone and watch him in action.
Despite the fact that Norwich agreed to pay a £5m fee for the midfielder, they will now no longer be pursuing a deal.
The Canaries are currently on the lookout for a new central midfielder after sanctioning a departure for Pierre Lees-Melou.
Lees-Melou sealed a permanent move to French outfit Stade Brestois last week after featuring for Norwich in the Premier League last season.
Kone, who has earned two caps at international level for Canada, has played regularly for CF Montreal this year.
Norwich have already bolstered their squad in the current transfer window by securing the services of Isaac Hayden and Gabriel Sara.
The Canaries are set to make their return to Championship action on Saturday when they face Cardiff City.
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No longer set to seal a move for Kone, it will be interesting to see whether Norwich are able to sign another central-midfielder between now and the start of September.
It could be argued that head coach Dean Smith may find it beneficial to switch his focus to signing an individual who has a proven track-record of delivering the goods in the Championship.
By nailing their recruitment, the Canaries could potentially bolster their chances of fighting for a top-two finish in this particular division.
Having previously led Aston Villa to the Premier League in 2019, Smith will be determined to replicate this feat at Carrow Road next year.