Norwich have been looking for a new coach in recent weeks after Liam Manning was sacked following a string of poor performances that have left Norwich below the relegation zone.
Former Danish international striker Tomasson was believed to be one of three candidates left for the job after ex-Wolves boss Gary O'Neill was ruled out on Sunday.
Tomasson has allegedly held talks with the majority shareholder, Mark Attanasio, but Tomasson apparently chose to turn down the opportunity to become the coach of Danish compatriots Oscar Schwartau, Mathias Kvistgaard, Emiliano Marcondes, and Pelle Mattson.
Tomasson, who also has a past as coach of Blackburn, who also play in the Championship, has been out of work since he was fired as Swedish national coach in October.
The Canaries currently lie 23rd in the Championship table, as fans fear that Norwich may be relegated to League One for the first time in 17 years.