The former Netherlands international last week told the BBC's World Football show that he could see himself taking charge of either the London club or Liverpool in the future.
And Tottenham head coach Sherwood, who was only appointed as Andre Villas-Boas' successor in December, was disappointed with the 43-year-old's public declaration of his interest in taking the top job at White Hart Lane.
He said: "It's natural I suppose, it's a big job, but I don't think I would ever tout myself about for a job when someone was already in the hot seat,
"But if they want to do that, that's up to them. I don't know Frank. I’m not sure. I’m relaxed about it. But it wouldn't be something I would be doing.
"They just want to put themselves in the frame. Obviously they are not happy with the jobs they are doing if they are touting themselves for the Tottenham job."
De Boer's Ajax side sit top of the Eredivisie and although he has no intention of leaving the club for the time being, he revealed that a move to the Premier League appeals.
"Those two clubs (Liverpool or Tottenham) are clubs that I think in the future I could be a manager of," De Boer told the BBC.
"I think the history of the clubs and what you can do with the team is my cup of tea.
"(But now) I'm not really thinking about it because I'm very happy here at Ajax. I'm not in a hurry to leave because everybody is still happy with me.
"I step in my car with a big smile to go to the club. I don't think I'm finished here but there will come a time when I don't like it any more or the club doesn't like me anymore.
"Then we have to go both ways."
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