The Belgian, who had an impressive 2012-13 campaign as the Amsterdam outfit lifted the Eredivisie title, has caught the attention of the Canaries, according to his representative
The 24-year-old centre-back made 45 appearances for the club in all competitions last season as Frank de Boer's side lifted the Eredivisie title.
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“I understand they made contact with Marc Overmars [Ajax's director of football],” Alderweireld's agent, Soren Lerby, told De Telegraaf.
“Toby has left the pre-season camp of Ajax in Austria due to personal reasons and I haven't spoken with him about Norwich yet.
“I don't know if Toby is interested in a move or not.”
Chris Hughton has been busy in the transfer market so far, securing the services of Javier Garrido, Ricky van Wolfswinkel and Nathan Redmond.
Should Alderweireld follow the trio to Carrow Road, Ajax boss De Boer is convinced the club have enough quality in their ranks to cope without him.
“If Toby would leave, then we have with Joel Veltman and Van der Hoorn two good players who could take over that position,” said the 43-year-old.