Carroll has failed to score in the league this season and this baron run has seen many question his record-breaking £35m transfer fee.
Enrique, who also played with Carroll at Newcastle, predicts the England striker can win Liverpool fans over with a goal against fierce rivals Everton.
"The derby is a massive game. Against Everton would be the perfect game for him to score."
Enrique followed Carroll to Anfield for a reported £6m fee in the summer.