The Spaniard has developed a good understanding with the 29-goal striker and provided another assist for the Barclays Premier League's leading scorer against Tottenham on Sunday. Enrique sees similarities with the bond he struck with another Uruguayan, Diego Forlan, when the two played together at Villarreal. And he likened Suarez's influence on Liverpool with that of Messi's for Barcelona.
"If you are good players you understand each other," said the defender, who is enjoying a good run of form since returning as first-choice left-back, after it had appeared his Anfield future was in doubt during the first half of the season. He added:
"When I was at Villarreal with Forlan I linked up really well with him as well.
"In the game all the time the first person I look for is him (Suarez) and he always makes a movement and I try to put the ball there and he does the rest.
"It is really easy to understand with him. He is our best player and he can do something from nothing.
"It's like at Barcelona - the first player they look for when the game is in a bad situation is Messi because you know he can do something.
"Luis is the same - I look for him because I know he can do something different and we understand each other."
The victory over Spurs was seen as something of a watershed moment in terms of the side overcoming a perceived mental block in regards to recovering losing positions. Their 3-2 win over their third-placed opponents was only the second time this season Brendan Rodgers' team had come from behind to win in a league game. And when Spurs took a 2-1 lead at Anfield Enrique admits their previous poor record had him thinking a victory was unlikely.
"In the first half they killed us a little bit because they scored in the last minute," he said.
"It was a little bit bad at that point but the manager said some words in the dressing room to lift us.
"They scored again in the second half and, to be honest, I didn't think we would win the game
"The statistics speak for themselves - of course you want to win and we will try but for our mentality we don't have good experiences of this type when we are losing.
"But the team worked very hard and this is the important thing because when the team stick together you can see the results and the character from the team was really good."