Overnight reports claimed that Madrid are keeping tabs on Pochettino ahead of a potential summer swoop for the Argentine coach.
While the 41-year-old rubbished the reports, the Saints boss did not commit his long-term future to the Premier League outfit, who currently sit ninth in the table.
"You all know I am not one to speak about rumours, speak about unrealistic things, intangible things so I really have no comment on that," BBC Sport quotes Pochettino as saying.
"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."
Questions were raised over Pochettino's position at the club when Southampton chairman Nicola Cortese resigned, but the Argentine swiftly calmed fears that he was going to follow suit.