Manchester United have made Pochettino their top target to replace Jose Mourinho in the summer.
Mourinho was sacked on Tuesday and has been replaced by Ole Gunnar Solskjaer until the summer.
But it is understood United will launch a move for Pochettino between now and May and are not currently considering anyone else for the role.
Pochettino spoke on Tuesday before their game with Arsenal last night and refused to rule out leaving Tottenham.
However Tottenham’s head of communications Felstein refused to allow Sky Sports reporter Dharmesh Sheth to quiz Pochettino on the subject today in a stunning press conference.
Pochettino was facing the media to preview the game against Everton on Sunday.
And Sheth wanted to ask about the situation at Manchester United, before being stopped in his tracks by Felstein.
“Mauricio it won’t have escaped your attention that there is a lot of talk about yourself and Manchester United. Now the former technical director of Southampton Les Read,” Sheth said before being cut off.
“Dharmesh, we’ve gone over that,” Felstein said. “ Anything to do with Manchester United we’ve had 48 hours ago the same conversations. I’m not prepared to have another press conference dominated by it.
Mauricio Pochettino was not allowed to answer questions on Manchester United specualtion
Mauricio Pochettino was not allowed to answer questions on the situation
“It’s not being dominated by it,” Sheth responds. “I have to ask the question.”
Felstein then says: “I’m not prepared to have it again so I have to ask you to move on.”
Sheth tries again: “With respect everybody is talking about this.”
Felstein replies: “With respect we invite you here to preview a football match and you’re coming and asking the manager about another job.”
“It works both ways though,” Sheth interjects. “Other occasions you’d say ‘lets not talk about the football match’ because you want to get something else out. It works both ways, surely.”
“No,” Felstein replied. “Move it on please.”
Sheth then says: “Could I ask in that case, everything that’s happening at the moment, I just want to tell you what Les Read said.”
Mauricio Pochettino wasn’t allowed to talk about the Manchester United job
Mauricio Pochettino turns to look at Simon Felstein as he stops the Sky reporter asking the question
Mauricio Pochettino smirks as he is asked about the Manchester United job
“No,” Felstein says again. “I’m sorry.”
Pochettino then turns to Felstein, pats him on the arm and says laughing: “You’re going to be the star of this press conference.”
“Move it on please Dharmesh,” Felstein says.
“What I’m saying is this going to carry on for months Simon, “ Sheth said.
And Felstein said: “OK fine. Let people speculate. We’re not going to have our press conference dominated by it. There’s plenty else to talk about.”
Manchester United appointed Ole Gunnar Solskjaer as their caretaker manager this week
Jose Mourinho was sacked by Manchester United on Tuesday
Sheth said: “We’ve been talking about plenty else. I don’t understand. There’s a question that needs to be answered.”
Felstein finishes with: “OK can we have the cameras off for a second please.”
When Pochettino did finally answer some questions he praised Dele Alli’s reaction to the incident when he was hit by a bottle last night against Arsenal.
I think it was an amazing reaction,” he said. “In another country the player will be down on the pitch and create a big problem.
“He was so honest, professional and behaved really well. Arsenal must be grateful with him. Sometimes a player would have gone down and created a massive problem. Sometimes people have criticised him but it is good to praise him now.
“He is more mature now but still good – he is so young. He is still learning. I know Arsenal is going to take responsibility and fix the problem.”
Mauricio Pochettino praised Dele Alli for his behaviour against Arsenal
And he declared the Premier League title a two horse race between Liverpool and Manchester City.
“I agree,” he said. “Manchester City and Liverpool are at the top. They are the two big candidates to win the Premier League.
“We are in behind with some gap, we are there with Chelsea, Arsenal and [Manchester] United.
“There is still a long way until the end of the season but it is normal if people consider them the two bigger candidates to win the Premier League.
“Today, it is impossible to say if we are going to have the chance to fight for the title. The most important thing is to have the faith that we can compete.”
Tottenham will battle to keep Pochettino after getting him to commit to a new deal last summer.
However the feeling is that Pochettino would like the chance to speak to United when they make their move.
Solskjaer arrived at the United training ground today to take training for the first time and will hold a press conference tomorrow morning.