Former Espanyol head coach Pochettino has impressed during his time at St Mary's, taking a team three points clear of the relegation zone when he took over last season to ninth in the Premier League this time round.
That has led to him being linked with Real, should current incumbent Carlo Ancelotti leave the Bernabeu, and although he admitted the club should be flattered by the link he insisted that a move is not on the cards.
"I am not one to speak about rumours or unrealistic things so I have no comment on this," he said on Thursday.
"It is very flattering for Southampton as a football club and it is also very flattering for our players, they are the ones on the pitch making us so great.
"I also don't like to talk about the future - I am not one to talk about the long-term future.
"Real Madrid are an amazing club, a great club, and you never know what could happen in football.
"But at the moment I am really happy at Southampton."
Pochettino's current contract at Southampton runs until the end of next season and the Argentinian plans to assess his position over the summer.
He confirmed he has not spoken to non-executive chairman Katharina Liebherr since she first replaced Nicola Cortese and played down talk of a new deal, for now at least.
"I understand that the club is going through some changes at the moment," he added.
"The club needs some time to reorganise. It is a time of reorganisation at the club. Everyone needs time to adapt to their new roles.
"I also want to say I have until the end of this season and the next, so I still have some time left."
Meanwhile, Pochettino confirmed teenage striker Sam Gallagher will miss Saturday's game with Stoke City following the death of his father after a short illness.
"It is a very tough moment indeed and we will give him our full support," said Pochettino.
"Sam is going to be with his family until Monday. They need him to be present, they need to be united and together."