When Kenny Dalglish signed the Spaniard for £6million in the summer of 2011 the player's early performances appeared to suggest he had solved a long-term problem at left-back
However, his form dipped within about four months and come the start of this season it appeared the 26-year-old's future was in serious doubt under new manager Brendan Rodgers.
A knee injury curtailed his pitch time and he effectively lost his place to 19-year-old Andre Wisdom, who came in to cover for right-back Glen Johnson who was switched to the left.
But in the last few weeks Enrique has enjoyed something of a resurgence.
He has started the last five Barclays Premier League matches - having made only one previous start in the current campaign - and a new role as a midfielder brought his first goal for the club just over a week ago.
Boosted by his turnaround in fortunes Enrique remains confident he still has plenty to offer despite appearing not to fit into Rodgers' plans.
"Football is for moments and now I am playing well so I hope I can continue like this and help the team as much as possible," he said.
"Last year, up to December, I played really well and then I don't know why I dropped my form.
"Now I've started to do it again and it is more important to think in the present and live from now and I will try to do my best now.
"To be honest I've never been worried because I've always believed in myself.
"From the start (of this season) I had knee problems so I have to prove myself with the manager, you have to to that always.
"It is not what you did before, it is what you do now.
"Every time you have to play well - if not there are players who will play better than you so.
"But I am really happy here. It is the biggest club I've played for, the fans are amazing and I really like the city so of course I want to play here for a long time."
Despite apparently not initially impressing Rodgers Enrique, helped by injuries and the manager's occasional switches to a wing-back system, has played his way back into the side.
He produced another good display in Sunday's goalless draw at Swansea, unluckily having a goal ruled out for offside, and is enjoying working in Rodgers' new set-up.
"From the start he is the best manager I've had in England in terms of tactics and everything," said the former Villarreal and Celta Vigo defender.
"Tactically he is like the Spanish, it reminds me of what happened at Villarreal.
"He has a mentality like a Spanish manager and I really like that."
And despite preferring to play at left-back he has quickly got to grips with his more advanced role.
"I like to play there but to be honest my position is left-back, it is where I am more comfortable and is where I have been all my life in the Premier League," he added.
"Of course, you enjoy it when you attack and I don't have to defend that much and playing there with Luis (Suarez) is really easy as his movement is everything and he is a really clever player.
"But it depends on where the manager wants me to play - I don't care where.
"It is the manager's decision and if you are not happy you go. He preferred Glen or Stewart (Downing) before and I have to respect his decision.
"I did what I always did: train as hard as I could and to try to get my chance like I have now.
"I am playing now so I am happy but I still have to improve in myself."