The Dutch champions claim they have already had an enquiry from Spurs about De Boer's availability, but that was refuted by the Premier League club in midweek.
De Boer is favourite with the bookmakers to take over from Tim Sherwood, who replaced Andre Villas-Boas midway through the 2013-14 season, although there are reports in the Sunday newspapers they have switched their attention to Southampton manager Mauricio Pochettino.
Ajax celebrated their 33rd title on Saturday, finishing the season with a 2-2 draw against NEC Nijmegen, and De Boer talked about the possibility of a new challenge at a press conference afterwards.
"I'm not thinking about the future right now," De Boer told Sky Sports.
"I have no intention to leave the club. When Tottenham Hotspur maybe will come, I will talk - not only Tottenham maybe other clubs who I think I am interested in, I will listen.
"I am very happy here. On June 23 we start again our preparation. That is what I am thinking about, first I have to get a signal from other clubs and then I will see."
Former Liverpool midfielder Christian Poulsen, who captained Ajax on Saturday, thinks De Boer would be a success in England.
He said: "For me, he is a winner. Everybody who works with around him would say that. He's really professional, he has been building things up here the last four years at Ajax.
"Every year he puts something on, specialists for the physical and for the mind. He's a good coach but he is also good at leaving responsibility to others. I have only good things to say."