The Reds' boss has confirmed the Spaniard will be out of action after tearing his hamstring against QPR and will miss crucial games against both Manchester clubs and Arsenal
The Spanish full-back sustained the injury against QPR last Sunday and was forced off on 71 minutes after being unable to continue.
Now, the Reds boss has revealed that Enrique will be out for up to six full weeks, ruling him out of crucial away trips to Manchester United, Arsenal and Manchester City.
Meanwhile, Rodgers has also suggested that new signing Daniel Sturridge will not be fast-tracked into matches too soon.
When asked about the striker's fitness, Rodgers told reporters: "We'll assess that. He's been catching up in terms of his fitness. I'm not going to rush him."
The Liverpool manager also praised outgoing midfielder Joe Cole, who has signed for his former club West Ham on a free transfer.
Rodgers added: "He's a good guy. He's never been a minute's problem but Joe needed to play. He's going home."