Alderweireld, who can play at centre-half or right-back, has been linked with a move to the Premier League this summer after some impressive performances in the Eredivisie last season.
Bayer Leverkusen had appeared favourites to sign the 24-year-old but have reportedly dropped out of the chase, while the likes of Liverpool and Tottenham Hotspur had previously been credited with an interest.
But it is Norwich who are the latest English club to have been connected with a swoop for Alderweireld as they look to bolster their squad ahead of the new campaign.
The player's agent, Soren Lerby, told Dutch paper De Telegraaf: 'I understand they made contact with Marc Overmars (Ajax's director of football).
"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."
While it remains to be seen whether Alderweireld will leave Amsterdam this summer, Ajax are confident they would be able to cope if he does depart.
Having snapped up youngster Mike van der Hoorn from FC Utrecht, head coach Frank de Boer is happy with the defensive options at his disposal.
He said: "If Toby would leave, then we have with Joel Veltman and Van der Hoorn two good players who could take over that position."