Sherwood was handed an 18-month contract at White Hart Lane after replacing Andre Villas-Boas in December but he has been unable to push the club towards their aim of qualifying for the Champions League.
Goal confirmed early in April that Spurs are set to axe Sherwood at the end of the current campaign and De Boer - who guided Ajax to a fourth straight Eredivisie title this season - has opened himself up to a move to north London despite the club's denials.
Mauricio Pochettino is also high on Daniel Levy's list of targets and Goal understands that Spurs will step up their interest in the Southampton manager this week but Sherwood maintains that he is the right man for the job.
|5/6||Spurs are 5/6 with bet365 to beat West Ham on Saturday|
"Somewhere along the line someone is telling porkies; I don't know [whom] for sure.
"Tottenham are not making any comment on that until the season finishes so I'm just carrying on as I normally do, being as professional as I can and preparing the team."
Despite the doubt surrounding his position at the club, Sherwood is on course to steer Spurs to a club-record-equalling 72 points in the Premier League this season and is trying to stay focused on the task at hand.
"I've got two more games to go," he continued. "We've had a good run recently. If we can get maximum points then we will get a record amount of points for Tottenham, which is 72. It will just be a shame that we didn't start the season any better.
"I just get on with it. There's not a press conference I've done since I took over when another name hasn't been mentioned.
"I've just got to get on with the job. The fans deserve that. In my opinion we've got one of the best fans nucleus in the country. We've got 40,000 fans waiting for a season ticket. It's a huge club. They deserve a manager who will give 100 per cent to the cause.
"I haven't spoken to [the club's hierarchy]. They've made a statement saying there will be talks at the end of the season. We'll see where that takes us but, at the moment, I'm enjoying it. It's a great honour to be at this football club.
"It's a difficult time when I go into these press conferences and there are outside distractions but I really have to concentrate, for the sake of these great fans, on getting us maximum points."
Sherwood believes that Spurs should look to the example set by Liverpool with Brendan Rodgers. The 41-year-old endured a diffcult first season at Anfield but has guided the club to the top of the table this season.
"We'll just have to wait and see. It's harder and harder to get that Champions League spot," the Tottenham boss continued. "The emergence of Liverpool this season has been a real minus for us. They've given Brendan Rodgers the time to build. They finished seventh last year but they had the correct man - look at them now."
Spurs target De Boer described Spurs as a "sleeping giant" on Tuesday and said that he would welcome offers after the final game of the Dutch season, stating: "After the last match on May 3 I will think about this possibility. I will have talks and will listen to their offer. After that I will decide on how I feel."