Captain Steven Gerrard called on the Anfield club's American owners to tie Rodgers down to a new long-term contract earlier this week.
The Northern Irishman's current deal runs out at the end of next season and he admitted he did not see his future away from Merseyside's red half.
He said: "As a manager, you aim to earn the respect of the players; you don't necessarily need to be liked, just so long as you are respected.
"I feel really at home here, I can't really think of being anywhere else. This is a wonderful football club and hopefully as time goes on and the philosophy becomes second nature, we continue to do better and advance."
"It (Gerrard's plea) makes me very happy. He's the captain, who has been an iconic figure at this club for many years and has worked with so many great managers, so it's very nice for someone with such status to say those words."
The Reds climbed to second after the 3-0 victory over Manchester United at Old Trafford on Sunday and travel to the relegation-threatened Bluebirds on Saturday.
But Rodgers refused to be drawn on his club's Premier League title hopes in the Cardiff pre-match news conference, with the fixture being the first of nine remaining games for the Anfield outfit.
He said: "The focus is purely on Cardiff City. We had a wonderful result and performance at Old Trafford, like you say, but there hasn't been any talk of any title.
"The run-in for us is the next game, we've got tough games all the way through. We've got a very tough game against Cardiff.
"We've had some good results at home this season against some of the top teams but we know it's going to be a tough game and we'll speak about the run-in at the end of the season."
When pressed on his opinion over what points haul he thought would be required to secure Liverpool's first league crown since 1990, Rodgers added: "You probably think about it (points total) a lot more than I do, to be honest.
"It's obviously your guys' job to assess and analyse. For me it has always been about the next game.
"That might sound a bit boring, I maybe answer it in different ways, but it's the reality of where we're at.
"We can't talk about Sunderland next Wednesday when we've got a massive game on Saturday at three o'clock.
"It is fairly straightforward. I think it is great for the supporters to dream and I think they have great pride in what they are seeing.
"We have had a very good season, are second in the league, and our level of play is improving all the time but we haven't done anything yet."