Nuno is facing greater scrutiny following a 3-0 defeat to Manchester United at home on Saturday.
This has prompted talks between club chairman Daniel Levy and managing director of football over his future, according to The Telegraph, and there could be an immediate change.
Back-to-back defeats to United and West Ham have only increased the pressure on the Portuguese after 17 games of his tenure.
Levy, who will no doubt have heard fans calling for his exit, was said to be furious following the defeat and had already been concerned about the performances.
Fans booed Nuno after substituting Lucas Moura in the 52nd minute as chants of 'you don't know what you're doing' rang around the Tottenham Hotspur Stadium.
He spoke to talkSPORT after the match and was confident of being able to turn things around, although he might not get the chance to.
"We had a bad one. We didn't perform good today." he said.
"It was a bad performance. We had the ball but not shots on target and we were not accurate with the final pass.
"We were vulnerable, allowed counter attacks and did many things wrong."
He continued: "The fans we had today in the stadium don't see what they wanted to see. Instead, they want their team playing good and being better than the opponent.
"There's nothing else you can expect. They are going to boo. It's up to us. There's no words that is going to change the situation. Only hard work.
"Not with words, only with actions. The actions are next Thursday and then in the Premier League, only with actions.
"No words are going to take the anger out of our fans.
When asked if he thinks he can do it, Nuno said: "Of course. We have to ask them in a humble way to keep supporting us because we need them."
There are already a number of names linked with the job - some of which will be familiar after their search over the summer.
Graham Potter currently ranks as the 3/1 favourite, according to Betfair, while Leicester boss Brendan Rodgers is 5/1.
Antonio Conte, who is also said to be a target of Manchester United, is also 3/1 joint-favourite having also been first-choice over the summer.