The 32-year-old Belgium international is out of contract at the end of the current season and has yet to be offered a new deal by Spurs.
Vertonghen, who joined the club from Ajax for €12m in 2012, has struggled for form in recent weeks and appeared to cry when he was withdrawn in the second-half of Tottenham’s 3-2 FA Cup victory over Southampton last week.
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His agent, Tom de Mul, quickly insisted that Vertonghen was happy in north London but speculation over his future has been rife and now Ajax have confirmed they are considering bringing him back to Amsterdam.
“Jan has a history at Ajax,” the Dutch club’s manager, Erik ten Hag, told Ziggo Sport.
“Of course we are following his situation very closely, but you also have to look at the position in which someone plays.
“If that comes together, the availability and the position in which he plays, then he is an option.
“There is no question of any age limit here. If someone is good enough, it doesn’t matter how old he is.”
Vertonghen has made 22 appearances in all competitions for Tottenham this season.
However, he was an unused substitute for their last Premier League fixture – a 2-0 win over reigning champions Manchester City – with José Mourinho instead preferring 20-year-old Japhet Tanganga at left-back and 23-year-old Davinson Sánchez alongside Toby Alderweireld in central defence.