Spurs are expected to appoint a new manager in the summer after reports earlier this month that Sherwood would not complete the final year of his 18-month contract.
That deal was given to him in December following the sacking of Andre Villas-Boas - leaving chairman Daniel Levy searching for his 10th new manager in 13 years.
Tottenham insist no official approach has been made and told Sky Sports News: "There is nothing happening, we have a season to finish."
But Sky Sports News understands Spurs have told Ajax they are interested, and De Boer is one of a number of managers they are considering.
Spurs were heavily linked with Louis van Gaal until the sacking of David Moyes at Manchester United, with the Holland coach now backed to move to Old Trafford when his duties with the Dutch national team end after the World Cup in the summer.
De Boer and Southampton boss Mauricio Pochettino have since emerged as the leading candidates to take over at White Hart Lane, and De Boer, whose side clinched the Eredivisie title on Sunday for the fourth consecutive time, has admitted he is interested in a move to north London.
"Spurs have made an approach," he said. "I'm going to listen and talk. Then I'll make my feelings known.
"At this moment I have had absolutely no contact with other clubs. I've said to (director of football) Marc Overmars that until May 3 I'm not going to think about it - I'm busy with Ajax.
"I know that Tottenham are a beautiful club with a beautiful history. I want to add something to a club, so that people can say that they see the hand of Frank de Boer.
"Liverpool are a good example of this with Brendan Rodgers."