The Spanish side were searching for a replacement for Julen Lopetegui, and Pochettino was said to be high up on their wishlist.
However, Spurs held firm, and Pochettino insists that he was never distracted by the rumours.
“I am so focused on my job at Tottenham. A new rumour appear every day,” he said.
“That rumour you tell me and the opposite appeared 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 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.”
There were fears that Pochettino could depart, after he expressed his frustrations publicly about this season at Spurs.
Pochettino said he was enduring his worst period as Tottenham boss, despite his side making a strong start to the season, last month.
The uncertainty over Pochettino’s future seems to be over for now though, with Spurs still racking up wins over recent times.
Tottenham are next in action on Saturday, when they take on Crystal Palace at Selhurst Park.