Rodgers recently highlighted Enrique and fellow full-back Glen Johnson as the best in their respective positions in the Barclays Premier League.
Enrique told liverpoolfc.com: "I'm really grateful - I know he said that and you have to say thanks. We try to work as much as we can because football is not a present.
"You have to work every day; you are there now but if you drop your form, another player will take your position. I will try to stay there. I don't like to speak about myself but, for me, Glen is one of the best right-backs in the world."