Sherwood has lost just one Barclays Premier League fixture since replacing Andre Villas-Boas in December and has taken Spurs to within three points of a place in the top four.
The 45-year-old penned an 18-month contract when he took over from former manager Villas-Boas, but that did not stop Ajax coach De Boer telling the BBC's World Football Show that, along with Liverpool, Tottenham was a club he could fit into easily.
"Those two clubs are clubs that I think in the future I could be a manager of," he said.
"I think the history of the clubs and what you can do with the team is my cup of tea.
"Tottenham called my manager with the possibility after sacking Villas-Boas but I said, 'no, right now it's not the right moment'.
"I don't think I'm finished here (Ajax) but there will come a time when I don't like it any more or the club doesn't like me any more. Then we have to go both ways."
Sherwood, who takes his side to Newcastle on Wednesday evening looking to build on Sunday's 1-0 home win over fellow top-four hopefuls Everton, steered clear of haranguing De Boer's comments but said he understood why any manager would tout themselves for the Spurs job.
"I don't blame them," Sherwood said.
"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.
"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."
Sherwood knows reaching the Champions League was the target for his predecessor given the large investment in the squad in the summer after the sale of Gareth Bale to Real Madrid.
But the former Blackburn captain accepts even that may not be enough if chairman Daniel Levy decides he wants more.
"I am just going to do what I can," he added.
"I can assure everyone I will give 100 per cent to do my best for this football club. If that's not good enough, someone else comes in and gets the opportunity.
"I don't even know if top four gets me the job. You will have to ask the chairman but he doesn't give much away. You certainly wouldn't want to play poker against him."
"You need to just do as well as you can and hopefully someone thinks you are doing a good job. I don't think I could do a job if I wasn't enjoying it, even this one. If I wasn't enjoying it, I'd be gone. Listen, my life would be a lot easier if I wasn't manager of Tottenham, let me tell you that."