Spurs are eighth in the Premier League after losing five of their opening 10 matches following Nuno's appointment in the summer.
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Sources told ESPN chairman Daniel Levy is talking with footballing director Fabio Paratici on Sunday but is reluctant to make a knee-jerk decision so early in the campaign. However, the level of hostility from the club's supporters inside the Tottenham Hotspur Stadium this weekend is said to have surprised many senior figures at the club.
Chants of "You don't know what you're doing" were aimed at Nuno as he substituted Lucas Moura for Steven Bergwijn early in the second half before fans demanded "We want Levy out" and appeared to aim boos in the direction of club captain Harry Kane, who had his desired move to Manchester City blocked before the start of the campaign.
It is unclear at this stage whether Nuno will be sacked, but one source has claimed "all options are open" after a damaging result in which the team were booed off at half-time and full-time.
Asked after the game whether he was confident he would be given the time to turn things around, Nuno replied: "I'm only thinking about the next training session because there are no words that are going to solve the situation.
"The booing and disappointment of the fans is understandable. When they don't see the team that they expect -- and I truly expect we are better than we showed today -- they are going to boo. It is up to us to change the mood."
Tottenham declined to comment when ESPN contacted them.