Since leaving Anfield for Camp Nou in 2018, Coutinho has failed to established himself as a first-team player, instead spending this campaign on loan at Bayern Munich.
Although Barcelona are desperate to part ways with the Brazilian, they are yet to receive any official offers for his signature.
However, Enrique feels that the Premier League champions would only benefit from handing the 28-year-old a second spell on Merseyside.
Speaking to Stadium Astro, the former left-back said: "We need a playmaker, a number 10, who is going to be better than Coutinho for us? He knows the club, he knows the city, he's going to perform straight away because he's been a Premier League player.
"The only problem is wages-wise, I believe he's very, very high wages-wise in Barcelona, so I'm not sure if he will go to Liverpool obviously losing money.
"The problem with Barcelona, they try to play him on the left side all the time, in Neymar's position and he's not this type of player, he needs to play in the middle."
Between January 2013 and January 2018, Coutinho scored 54 goals from 201 appearances for Liverpool in all competitions.