The Belgium international, who can play at centre-half or right-back, has reportedly attracted the attention of several clubs after a series of impressive performances in the Eredivisie last season.
Norwich are understood to be keen on striking a deal but Alderweireld has not yet made his mind up on the best course of action for his career, and has suggested he could see out the final 12 months of his contract in Amsterdam.
"I am still at Ajax and I am happy here, maybe I will stay for a year," he told Dutch television station AT5.
"With every bid that comes, I see if it is good for me. Whether I will stay or not is something we'll have to see about.
"I'm not saying 'no' in advance to Norwich, but I am certainly not saying 'yes' immediately.
"Maybe I will stay a year, which could be for the best. The overall picture has to be right for me. Maybe that will be Norwich City or any other club."