Reports suggested Madrid offered the Argentine head coach a blockbuster deal to succeed Lopetegui, only for him to turn Los Blancos down.
And Pochettino, who signed a new long-term Tottenham contract this year, addressed the latest speculation when he appeared in front of the media on Thursday.
"Look, I am so focused on my job at Tottenham," said Pochettino. "A new rumour appears every day. That rumour you tell me and the opposite appeared [in the media] the other day. Many things happen.
"The most important thing is people need to know I am so focused on Tottenham, I am so responsible in my job and our fans need to know that and of course [chairman] Daniel Levy needs to know I am so focused on Tottenham, working so hard trying to help the club to achieve all that we want.
"Rumours are rumours and always happen, not only at Tottenham but every team. You can do nothing [about speculation]."
But Pochettino is hopeful Victor Wanyama and Eric Dier will be available for Saturday's Premier League match away to Crystal Palace.
"We hope that from the beginning of January he will be ready," Pochettino said of Dembele's injury. "After it's about the evolution, it's very dynamic the evolution and how he's going to recover.
"Always it's about the patient, the player, and how he's going to react after the injury. We hope he'll be back as soon as possible and early in January to help the team.
"Always you miss all the players when they are injured. We were talking before, in 13 days we play five games. It's less than three days, every two and a half days we're competing. It's a massive effort for the players. That is why I am so pleased.
"In the same way, I want to say some nice words to the staff, because they are helping the players to be ready in every single game. They work a lot and they don't have a rest. That is important to have nice words for them.
"Of course I think we have some players back like Eric Dier and Victor Wanyama, they've started training with the group and we'll see tomorrow if they can be available to be in the squad for Saturday."