Alderweireld has been linked with a move away from Ajax all summer, with the likes of Liverpool and Bayer Leverkusen credited with an interest in his services.
However, Norwich agreed a fee with Ajax to bring Alderweireld to Carrow Road, but were unable to agree personal terms with the Belgian international.
Alderweireld's agent, Soren Lerby, rejected suggestions that it was Norwich's standing in the game that persuaded the 24-year-old to reject their overtures.
"The problem was not that Norwich didn't fit Toby's ambitions, but we simply failed to agree terms," Lerby told Algemeen Dagblad.
Alderweireld, who is entering the final year of his contract at the Amsterdam ArenA, has admitted that if a move does not materialise this summer he is happy to stay Ajax.
"There is still other interest and a transfer takes a long time," Alderweireld told voetbal.nl. "We're only in mid-July it can still be done. If a nice club comes, it can go fast.
"If there is nothing, then I'll just stay at Ajax."