- Oops!Something went wrong.Please try again later.
Spurs on Tuesday appointed Ryan Mason as interim head coach until the end of the season following Mourinho's sacking and have begun searching for a new permanent boss.
Rodgers has admirers in the north London club's boardroom but the cost of recruiting him from Leicester, where he earns a reported £10million-a-year and has a contract until 2025, would likely be prohibitive.
And Rodgers told reporters: "It's football, there is always speculation around, every job which comes up there will always be different managers speculated to go in.
"Tottenham is a fantastic club, it's a huge club but my focus is here. I'm at a world-class training facility, the project we're in here we still want to develop and have a lot of work to do.
"I have a great connection with the players, the board and we have plans to keep progressing.
"While I have the energy, the happiness and see that challenge continuing I'm very happy to be here. You can't stop gossip but I don't think about it."
RB Leipzig boss Julian Nagelsmann has emerged as Tottenham's first choice to replace Mourinho, who was dismissed on Monday with the club seventh in the table ahead of Wednesday night’s visit of Southampton.
Rodgers learned the ropes under Mourinho during the Portuguese's first spell at Chelsea and says the 57-year-old's quality should not be in doubt, despite a difficult spell at Spurs.
"Jose is a world-class manager," Rodgers said.
"The thing which disturbs me a little is how it gets questioned. What he has done in the game, he should be able to position the expectations. He has earned that respect to be able to do that.
"You are not a world-class manager one day and then you go to a job and it doesn't quite work out and you're not. He is clearly a winner, he will always be a winner.
"I'm disappointed for Jose, I know him personally and know he is a world-class manager, he has shown that over his career.
"He is a manager who has won and unfortunately for him that hasn't happened at Tottenham.
"Their expectation is to win titles and compete at the top end of the league. I have empathy for any manager who loses their job."