Mourinho has been without a job since his unceremonious sacking by AS Roma in January and there has been speculation over the Portuguese returning to Chelsea for a third stint.
When asked about the possibility of Mourinho replacing him as Chelsea boss manager, Pochettino said: "I respect Jose. He’s my friend and he was amazing for this club. Circumstances are circumstances. We need to keep pushing, believing in ourselves, and accepting all the things that come from the fans. Of course, I respect the fans.
"You need to ask the players. If the players believe they’ll do better with another coach, I am the first to say: ‘Hey, they can go and talk with the owner and the sporting director'."
The Argentina coach added: "Do you see me worried about this? No. Look, is attitude a problem? No. They [the players] are clever enough; you can see in the way they behave and everything that they are behind us. There is no doubt. I came here because I knew that it was going to be tough but also knew we were going to need time and belief.”