Rodgers has been linked with Arsenal this week.
"If you work well, it's a natural consequence of what happens in this game - you'll get linked to other jobs," he told Sky Sports.
"People link me, at times, to top clubs - I'm already in a top job. This is a fantastic club, a great job for me and in this moment with the ownership we have, the players I have, I'm absolutely loving every minute of it.
"All the gossip and speculation, whether it's for you or against you, is part of the game."