Tim Sherwood took charge of Spurs for Wednesday's 2-1 loss to West Ham in the Capital One Cup, and could get the job permanently if he impresses.
But Guido Albers told Voetbal International that despite there being no official approach, he is aware of Spurs' interest in the De Boer.
"Through several channels it became clear to me that Spurs would have an interest," he revealed. "But the club did not come to Ajax. So from our point of view there's not much to say about it. Frank isn't even thinking about it. He's fully focusing on Ajax."
De Boer is regarded as one of Europe's brightest young coaches, having led Ajax to three consecutive Eredivisie titles and a series of impressive displays in the Champions League.
Any move to White Hart Lane would see the Dutchman reunited with former Ajax stars Jan Vertonghen and Christian Eriksen.