The left-back, who expressed his desire to leave Newcastle, turned down possible moves to clubs around Europe.
The 25-year-old is expected to sign a long-term deal at Anfield after a fee was agreed with Newcastle for the Spaniard.
"I have rejected good offers from other leagues to stay in England," The Mirror quotes Enrique as saying. "The style of football here is perfect for me and I want to improve myself as a player.
"I always wanted to go to Liverpool and they were always my first choice.
"One of my ambitions is to play regularly for Spain and it's more realistic for me to fight for a place with Liverpool than with Spain."
Enrique is expected to agree personal terms and put pen to paper on a contract with the Reds in the next few days.