The former Argentina international has been in charge at the Vicente Calderon for almost 12 months and led them to a Europa League triumph last season, and he admitted he feels very loyal towards Los Rojiblancos.
"I would never coach Real Madrid because I’m sentimental about the old things. I must be mad but it lives in my heart what I feel for this football club," he told Rock and Closs.
"I have a contract until the end of the season and if you know me then you know I go on feelings. At the moment I feel good and I hope we can continue game by game, achieving what I’ve always wanted for Atletico.”
The European Super Cup winners are currently second in La Liga but only trail leaders Barcelona on goal difference, and Simeone singled out his players for the start they have made to the season.
"The credit goes to the players and we have taken advantage of the different characteristics they possess. What we have is a strong squad, which is shown by the way in which we have scored goals," he explained.
"Today we have more goals in us as Raul Garcia has come back from Osasuna and because [Diego] Costa stayed before [Eduardo] Salvio left, which gives [Radamel] Falcao and Adrian [Lopez] many more goalscoring opportunities."
Simeone reserved special praise for Colombia striker Falcao, who has been rumoured to have interested English sides Chelsea and Manchester City amongst others, but he refused to reveal whether the forward would be on his way out of the club in January.
"Radamel excites you," he added.
"All that happens with him is not accidental. He looks for things, he wants things and he trains to be the best. I think he knows that this is an important time and I am convinced that right now he is at a club that is stronger than any other.
"I’m not thinking of when he will go. It’s like anything else in that you have to enjoy it, live it, and whatever else happens will happen.
"Is there a replacement for him? He is different from the rest. He is a predator, aggressive, committed to working for the team; a very complete player.
"Knowing his potential he is somebody who will improve on his weaknesses because he knows what he is good at and what he is bad at. That is a great strength Falcao has."
Someone who was more sure of the striker's future was Atletico's general manager Miguel Angel Gil Marin, who insisted that the 26-year-old will remain with Simeone's team until the end of the season, despite the fact that his sale would wipe out the club's current debt.
"Falcao will carry on here, certainly until the end of the season. He will be staying and so will everyone else, the coach wants to stay and will also do so," he explained to El Partido de las Doce.
"In Europe there are 50 clubs with higher earnings than us and if we sold Falcao for €60 million (£48m) then yes it would solve our debts."