The full-back has compared his team-mate to the four-time Ballon d'Or winner due to his ability to produce "something from nothing" to help his side out of a tight spot
The Uruguayan is the Premier League top goalscorer with 22 strikes in 28 appearances this season, including opening the scoring and winning the decisive penalty in Sunday’s 3-2 win over Tottenham.
And Enrique believes Suarez is becoming the player his Liverpool team-mates look to when they require an added spark to turn a game in their favour - much like Messi and Barcelona.
"In the game all the time the first person I look for is [Suarez] and he always makes a movement and I try to put the ball there and he does the rest," Enrique told reporters. "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 win over Tottenham marked just the second time Liverpool had come from beyond to win under Brendan Rodgers in the league, and just the second top-10 side they have beaten.
And Enrique admitted that Jan Vertonghen’s goals either side of half-time to hand Spurs the lead prompted fears of another defeat, but believes an improved character saw the tie swung back in Liverpool’s favour.
"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."